David Arnold

Mathematics

• Department Home Page
• myCR
• WebAdvisor
• Optimath
• David Arnold Home

Math 30: Homework Assignments

There are files on this site in PDF format. You will need to download a free copy of the Adobe Reader to read them. Click the following icon to obtain a free copy of the Adobe Reader.

It is important that you have the most current version of the Adobe Reader that your system will allow. The above links will take you to the Adobe site. The Adobe site will analyze your system, but you may be asked to choose the appropriate version of the reader for your system. If this happens, carefully select the appropriate version of the reader.

Assignments and activities will be accumulated on this page throughout the semester. Please return often as this page will be updated frequently.

Directions: Please follow these directions on all homework assignments.

1. It is recommended, but not required, that you do all of your homework on engineering graph paper (available in the bookstore).
2. On each homework assignment, place your name in the top right corner of the page.
3. On the first line of the of the first page of your homework, please write down the assignment number, the pages that encompass the assignement, and list each exercise number assigned. For example, the first line of your homework might read:

   Assignment #12, Page 150, #1, 3, 5, 7, 8, 10, 11, 23, 45

4. If an assignment takes more than a page, please staple the pages together with a single staple in the upper left-hand corner.
5. Simple one or two word answers or choices without explanatory prose are not acceptable. In all cases, use sound writing to justify your response.
6. Please do not do computation for a problem on one sheet of paper, then refer to a graph or diagram on another sheet of paper near the end of your stapled packet. Keep your work together, compuations and graphs and diagrams in the same general neighborhood on your homework.
7. Please do not crowd your work on your paper. Space things out and avoid tiny diagrams that are hard to read (please be nice to my old eyes).
8. Assignments will be handed in during classtime in separate piles: the assignment #1 pile, the assignment #2 pile, etc., so please do not staple two or more assignments together.

Spring 2009

• Assignment #0 (Due Friday, Jan. 23)
  • Blackboard: Click the Blackboard icon that follows. This will initiate contact with BlackbBoard. Read the Student Introduction, User Name and Password, and Getting Help sections. Read the Updating Student Information section and adjust your personal information. Be sure to write down your login name and password for future reference. It is extremely important that your email address is current!

  • 

  • Once you login to Blackboard, locate your math class and take some time to find out what is provided. Then read the "Welcome Message" in the Discussion Board and reply to to the "Welcome Message" thread. In the future, use the Discussion Board to discuss issues and problems you are having with your class.
• Assignment #1 (Due Monday, Jan. 26)
• • Make sure the latest version of the Adobe Reader that can be supported by your system is installed on your computer. After installation, open the Adobe Reader and when prompted "do you want to make this application the default reader for PDF files," answer "Yes." This is especially important on the Macinstosh, otherwise OPTIMATH quizzes will open in Preview and will not work properly.
  • Read Introduction to Optimath.
  • Watch the video Logging on to Optimath.
  • If your name has a hyphen, apostrophe, or space, watch the video Logging on to Optimath (Special Names).
  • Go to Optimath, select the link Math 30, E1983, David Arnold, and log in.
    • Note: Macinstosh users must use the Safari browser. Firefox does not work with Adobe Reader or the Optimath system on the Macintosh.
  • Complete the quiz "Test your Browser."
• Assignment #2 (Due Monday, Jan. 26)
• • Read Writing Mathematical Formulas in Optimath.
  • Watch these videos:
    1. Interval Notation (Part 1).
    2. Interval Notation (Part 2).
    3. Interval Notation (Part 3).
    4. Rational Expressions.
  • Try your hand at "inline expressions" using our Syntax Checker. Note: Both Mac and Windows users must open the syntax checker application in Firefox.
  • Go to Optimath, select the link Math 30, E1983, David Arnold, and log in.
    • Note: Macinstosh users must use the Safari browser. Firefox does not work with Adobe Reader or the Optimath system on the Macintosh.
  • Complete the quiz "First Practice."
• Assignment #3 (Due Friday, Jan. 23)
• • Sullivan Edition 7 (Chapter 1, Section 1)
  • • Use a purely algebraic technique to solve the equations in exercises: #31, 35, 42, 43, 46, 52, 55, 58, 64, 72, 73, and 75.
    • Use a purely algebraic technique to solve the equations in exercises #77, 78, and 81 for the requested variable.
    • Download and read Example 5 and use the guidelines listed in "Summary 7" to solve the equations in exercises #22 and 37 graphically. PLease summarize your graphical solution as shown in Figure 11 of the above reading. When your graphing solution is complete, solve the given equation a second time, using a strictly algebraic technique. Put your solutions side-by-side on graph paper.
  • Sullivan Edition 8 (Chapter 1, Section 1)
  • • Use a purely algebraic technique to solve the equations in exercises: #31, 35, 42, 43, 46, 52, 55, 58, 64, 72, 73, and 75.
    • Use a purely algebraic technique to solve the equations in exercises #77, 78, and 81 for the requested variable.
    • Download and read Example 5 and use the guidelines listed in "Summary 7" to solve the equations in exercises #22 and 37 graphically. PLease summarize your graphical solution as shown in Figure 11 of the above reading. When your graphing solution is complete, solve the given equation a second time, using a strictly algebraic technique. Put your solutions side-by-side on graph paper.
• Assignment #4 (Due Friday, Jan. 30)
• • Sullivan Edition 7 (Chapter 1, Section 2)
  • • Solve each of the following exercises by factoring and using the zero product property: #15, 20, 27, and 28.
    • Solve each of the following exercises by using the square root method: #32 and 34.
    • Solve each of the following problems by using the method of completing the square: #41, 42, and 46.
    • Use the quadratic formula to solve each of the following exercises: #55, 56, and 63. Your final answer must satisfy the three rules for "simple form:"
      1. If you can factor out a perfect square, you must.
      2. No fractions under a radical.
      3. No radicals in the denominator.
    • Use the discriminant to predict the number of solutions in exercises #87, 88, and 89 without actually solving the problem.
    • Find the value of k requested in exercise #112.
    • Download and read Example 8. Follow the technique shown in Example #8 to find the zeros for the equations in exercises #47 and 48. When your graphing solution is complete, solve the given equation a second time, using a strictly algebraic technique. Put your solutions side-by-side on graph paper.
  • Sullivan Edition 8 (Chapter 1, Section 2)
  • • Solve each of the following exercises by factoring and using the zero product property: #15, 20, 27, and 28.
    • Solve each of the following exercises by using the square root method: #32 and 34.
    • Solve each of the following problems by using the method of completing the square: #41, 42, and 46.
    • Use the quadratic formula to solve each of the following exercises: #55, 56, and 67. Your final answer must satisfy the three rules for "simple form:"
      1. If you can factor out a perfect square, you must.
      2. No fractions under a radical.
      3. No radicals in the denominator.
    • Use the discriminant to predict the number of solutions in exercises #93, 94, and 95 without actually solving the problem.
    • Find the value of k requested in exercise #122.
    • Download and read Example 8. Follow the technique shown in Example #8 to find the zeros for the equations in exercises #47 and 48. When your graphing solution is complete, solve the given equation a second time, using a strictly algebraic technique. Put your solutions side-by-side on graph paper.
• Assignment #5 (Due Monday, Feb. 2)
• • Sullivan Edition 7 (Chapter 1, Section 3)
  • • Simplify the expression in exercise #9. Place your answer in the form a + bi. On graph paper, sketch your answer as a vector in the Argand plane, then find its length or modulus.
    • Simplify the expressions given in exercises #12, 15, 18, 20, 23, 26, 27, 34, 35, 41, 46, 48, and 51. Place your final answer in the form a + bi.
    • Use a purely algebraic technique to solve the equations in exercises #56, 58, 61, 68, and 72. Place your final answer in the form a + bi.
    • Use an algebraic approach to solve the equations in exercises #67 and 69. On graph paper, sketch your solutions as vectors in the Argand plane and find their lengths or moduli.
    • Simplify the expressions in exercises #81, 82, and 83.
    • Provide proofs of the properties listed in exercises #87 and 88.
  • Sullivan Edition 8 (Chapter 1, Section 3)
  • • Simplify the expression in exercise #9. Place your answer in the form a + bi. On graph paper, sketch your answer as a vector in the Argand plane, then find its length or modulus.
    • Simplify the expressions given in exercises #12, 15, 18, 20, 23, 26, 27, 34, 35, 41, 46, 48, and 51. Place your final answer in the form a + bi.
    • Use a purely algebraic technique to solve the equations in exercises #56, 58, 61, 68, and 72. Place your final answer in the form a + bi.
    • Use an algebraic approach to solve the equations in exercises #67 and 69. On graph paper, sketch your solutions as vectors in the Argand plane and find their lengths or moduli.
    • Simplify the expressions in exercises #81, 82, and 83.
    • Provide proofs of the properties listed in exercises #89 and 90.
• Assignment #6 (Due Wednesday, Feb. 4)
• • Sullivan Edition 7 (Chapter 1, Section 4)
  • • Download Example 16 and study Example 16. Follow the lead in this example to find a solution for exercise #27 with your graphing calculator. Sketch the result on graph paper, then find a purely algebraic solution. Place your two solutions (graphical and algebraic) side-by-side on your graph paper.
    • Use a purely algebraic approach to find solutions for the equations in exercises #23, 25, 30, 35, and 38.
    • Make an appropriate substitution to change the equations in exercises #43, 46, 57, 60, 67, 68, 87, and 89 into quadratic form. Then solve the resulting equation. Be sure then to take these results and use them to continue on for solutions for the variable x.
    • For the equations in exercises #76, 77, 79, and 86, provide two solutions:
      1. Use the root or intersect utility on your graphing calculator to find the solution. Sketch the graph on graph paper, then mark the solutions on the x-axis of your sketch.
      2. Provide a purely algebraic solution.
      Place the two solutions side-by-side on your graph paper.
  • Sullivan Edition 8 (Chapter 1, Section 4)
  • • Download Example 16 and study Example 16. Follow the lead in this example to find a solution for exercise #27 with your graphing calculator. Sketch the result on graph paper, then find a purely algebraic solution. Place your two solutions (graphical and algebraic) side-by-side on your graph paper.
    • Use a purely algebraic approach to find solutions for the equations in exercises #23, 25, 30, 35, and 38.
    • Make an appropriate substitution to change the equations in exercises #43, 46, 57, 60, 67, 68, 89, and 91 into quadratic form. Then solve the resulting equation. Be sure then to take these results and use them to continue on for solutions for the variable x.
    • For the equations in exercises #76, 77, 79, and 86, provide two solutions:
      1. Use the root or intersect utility on your graphing calculator to find the solution. Sketch the graph on graph paper, then mark the solutions on the x-axis of your sketch.
      2. Provide a purely algebraic solution.
      Place the two solutions side-by-side on your graph paper.
• Assignment #7 (Due Friday, Feb. 6)
• • Sullivan Edition 7 (Chapter 1, Section 5)
  • • Download Example 8 and study Example 8. Follow the lead in this example to find solutions for exercises #55 and 66 with your graphing calculator. Sketch the result on graph paper as shown in Example 8; i.e., shade and label your solution on the x-axis. Next, find a purely algebraic solution. Draw a second number line and shade the solution on this number line. Place your two solutions (graphical and algebraic) side-by-side on your graph paper, then describe your solution using both set-builder and interval notation.
    • Use a purely algebraic approach to find solutions for the inequalities in exercises #58, 62, 69, 72, 75, 79, 82, 83, 86, and 87. Sketch your solution on a number line and describe your solution using both set-builder and interval notation.
  • Sullivan Edition 8 (Chapter 1, Section 5)
  • • Download Example 8 and study Example 8. Follow the lead in this example to find solutions for exercises #55 and 66 with your graphing calculator. Sketch the result on graph paper as shown in Example 8; i.e., shade and label your solution on the x-axis. Next, find a purely algebraic solution. Draw a second number line and shade the solution on this number line. Place your two solutions (graphical and algebraic) side-by-side on your graph paper, then describe your solution using both set-builder and interval notation.
    • Use a purely algebraic approach to find solutions for the inequalities in exercises #58, 62, 69, 72, 75, 79, 82, 83, 86, and 87. Sketch your solution on a number line and describe your solution using both set-builder and interval notation.
• Assignment #8 (Due Friday, Feb. 6)
• • Sullivan Edition 7 (Chapter 1, Section 6)
  • • Download Example 8 and study Example 8. Follow the lead in this example to find solutions for exercises #10 and 29 with your graphing calculator. Sketch the result on graph paper as shown in Example 8; i.e., shade and label your solution on the x-axis. Next, find a purely algebraic solution. Place your two solutions (graphical and algebraic) side-by-side on your graph paper.
    • Use a purely algebraic approach to find solutions for the equations in exercises #19, 21, 24, 28, and 30.
    • Download Example 7 and study Example 7. Follow the lead in this example to find solutions for the inequalities in exercises #38 and 43; i.e., shade and label your solution on the x-axis. Next, find a purely algebraic solution. Place your two solutions (graphical and algebraic) side-by-side on your graph paper.
    • Use a purely algebraic approach to find solutions for the equations in exercises #31, 34, 37, 41, 44, and 46. Draw a number line and shade your solution on a number line, then describe your solution using both set-builder and interval notation.
  • Sullivan Edition 8 (Chapter 1, Section 6)
  • • Download Example 8 and study Example 8. Follow the lead in this example to find solutions for exercises #10 and 29 with your graphing calculator. Sketch the result on graph paper as shown in Example 8; i.e., shade and label your solution on the x-axis. Next, find a purely algebraic solution. Place your two solutions (graphical and algebraic) side-by-side on your graph paper.
    • Use a purely algebraic approach to find solutions for the equations in exercises #19, 21, 24, 28, and 30.
    • Download Example 7 and study Example 7. Follow the lead in this example to find solutions for the inequalities in exercises #42 and 47; i.e., shade and label your solution on the x-axis. Next, find a purely algebraic solution. Place your two solutions (graphical and algebraic) side-by-side on your graph paper.
    • Use a purely algebraic approach to find solutions for the equations in exercises #35, 38, 41, 45, 47, 48, and 50. Draw a number line and shade your solution on a number line, then describe your solution using both set-builder and interval notation.
• Assignment #9
• • Sullivan Edition 7 (Chapter 3 Section 1)
  • • Do exercises: #28, 49, 54, 58, 68, 71, 72, 73, 75, 78, and 80.
  • Sullivan Edition 8 (Chapter 3, Section 1)
  • • Do exercises: #40, 49, 54, 58, 68, 71, 72, 73, 75, 80, and 82.
• Assignment #10
• • Sullivan Edition 7 (Chapter 3 Section 2)
  • • Do exercises: #9 and 10.
    • Consider the function f(x)=x²-3.2x-8.9. Use your graphing calculator to solve the equation f(x)=0. Report your solution as shown in class, shading and labeling the solutions on the x-axis. Don't forget those vertical dashed lines through the x-intercepts.
    • Consider the function f(x)=9.3-2.1x-x². Use your graphing calculator to solve the inequality f(x)>0. Report your solution as shown in class, shading and labeling the solutions on the x-axis. Don't forget those vertical dashed lines through the x-intercepts. Use interval notation to describe your solution.
    • Consider the functiona f(x)=11.2-5.x-x² and g(x)=12.x+2.35. Use your graphing calculator to solve the inequality f(x)<=g(x). Report your solution as shown in class, shading and labeling the solutions on the x-axis. Don't forget those vertical dashed lines through the points of intersection. Use interval notation to describe your solution.
  • Sullivan Edition 8 (Chapter 3, Section 2)
  • • Do exercises: #9 and 10.
    • Consider the function f(x)=x²-3.2x-8.9. Use your graphing calculator to solve the equation f(x)=0. Report your solution as shown in class, shading and labeling the solutions on the x-axis. Don't forget those vertical dashed lines through the x-intercepts.
    • Consider the function f(x)=9.3-2.1x-x². Use your graphing calculator to solve the inequality f(x)>0. Report your solution as shown in class, shading and labeling the solutions on the x-axis. Don't forget those vertical dashed lines through the x-intercepts. Use interval notation to describe your solution.
    • Consider the functiona f(x)=11.2-5.x-x² and g(x)=12.x+2.35. Use your graphing calculator to solve the inequality f(x)<=g(x). Report your solution as shown in class, shading and labeling the solutions on the x-axis. Don't forget those vertical dashed lines through the points of intersection. Use interval notation to describe your solution.
• Assignment #11 (Due Feb. 18)
• • Sullivan Edition 7. Read Chapter 3 Section 3.
  • • Perform the following tasks for exercises #22, 25, 27, and 32.
      1. Copy the given graph onto a sheet of graph paper.
      2. Answer the questions posed in the exercise.
    • For exercises #47, 48, 49, 57, and 58, perform each of the following tasks:
      1. Use algebra to show that f(-x)=f(x), f(-x)=-f(x), or neither.
      2. Sketch the graph on your calculator then copy the image onto graph paper.
      3. Use the previous two parts to determine whether the function is even, odd, or neither. Label your graph with your conclusion.
    • Perform each of the following tasks for exercise #63 and 66.
      1. Sketch the graph on your calculator, adjust the window to show all turning points of the graphs, then copy the result onto graph paper.
      2. Use the maximum and minimum utilities on your calculator to find the local extrema of the given function. Label your graph with these results and classify each extrema as a relative max or min.
      3. On your plot, state the intervals on which the function is increasing and decreasing.
    • For exercises #38 and 39, perform each of the following tasks.
      1. Find the average rate of change and the equation of the secant line as requested in the exercise.
      2. Use your graphing calculator to sketch the function and the secant line. Copy the result onto graph paper.
    • Perform each of the following tasks for the function f(x) = x² + 2x.
      1. Compute the slope of the secant line through the points (x, f(x)) and (x+h, f(x+h)), using:

         m_sec=[f(x+h)-f(x)]/h.

      2. Find m_sec for h = 0.5, 0.1, and 0.01 at x = 1. What value does m_sec approach as h approaches zero?
      3. Find the equation of the secant line at x = 1 and h = 0.01.
      4. Use a graphing calculator to graph f and the secant line on the same viewing window. Copy the result onto graph paper.
  • Sullivan Edition 8. Read Chapter 3, Section 3)
  • • Perform the following tasks for exercises #22, 25, 27, and 32.
      1. Copy the given graph onto a sheet of graph paper.
      2. Answer the questions posed in the exercise.
    • For exercises #34, 35, 43, and 44, perform each of the following tasks:
      1. Use algebra to show that f(-x)=f(x), f(-x)=-f(x), or neither.
      2. Sketch the graph on your calculator then copy the image onto graph paper.
      3. Use the previous two parts to determine whether the function is even, odd, or neither. Label your graph with your conclusion.
    • Perform each of the following tasks for exercise #49 and 52.
      1. Sketch the graph on your calculator, adjust the window to show all turning points of the graphs, then copy the result onto graph paper.
      2. Use the maximum and minimum utilities on your calculator to find the local extrema of the given function. Label your graph with these results and classify each extrema as a relative max or min.
      3. On your plot, state the intervals on which the function is increasing and decreasing.
    • For exercises #59 and 62, perform each of the following tasks.
      1. Find the average rate of change and the equation of the secant line as requested in the exercise.
      2. Use your graphing calculator to sketch the function and the secant line. Copy the result onto graph paper.
    • Follow the directions given in the text for exercise #75. Copy the graph found in part(d) onto graph paper.
• Assignment #12 (Due Feb. 20)
• • Sullivan Edition 7. Read Chapter 3 Section 4.
  • • Perform each of the following tasks for exercises #25 and 26.
      1. Copy the given function onto graph paper.
      2. Answer each of the questions posed on your graph paper.
    • Perform each of the following tasks for exercises #29, 32, 33, and 34.
      1. Copy the given function onto graph paper.
      2. Sketch the graph of the given function on graph paper.
    • Perform each of the following tasks for exercises #41 and 42.
      1. Copy the given graph precisely on graph paper.
      2. Determine an algebraic piecewise definition for the given graph. Place your result near your graph on your graph paper.
    • The following problems are not in the text. If you'd like more support for doing these problems, consider Chapter 4, Section 2 of our intermediate algebra text.
      1. f(x) = x + |x|
      2. f(x) = |x + 1| + |x - 3|
      3. f(x) = |x| - |x - 5|
      In each case, perform each of the following tasks:
      • Determine an algebraic piecewise definition for each function.
      • Sketch the resulting piecewise function on graph paper.
  • Sullivan Edition 8. Read Chapter 3, Section 4)
  • • Perform each of the following tasks for exercises #25 and 28.
      1. Copy the given function onto graph paper.
      2. Answer each of the questions posed on your graph paper.
    • Perform each of the following tasks for exercises #29, 32, 33, and 34.
      1. Copy the given function onto graph paper.
      2. Sketch the graph of the given function on graph paper.
    • Perform each of the following tasks for exercises #41 and 42.
      1. Copy the given graph precisely on graph paper.
      2. Determine an algebraic piecewise definition for the given graph. Place your result near your graph on your graph paper.
    • The following problems are not in the text. If you'd like more support for doing these problems, consider Chapter 4, Section 2 of our intermediate algebra text.
      1. f(x) = x + |x|
      2. f(x) = |x + 1| + |x - 3|
      3. f(x) = |x| - |x - 5|
      In each case, perform each of the following tasks:
      • Determine an algebraic piecewise definition for each function.
      • Sketch the resulting piecewise function on graph paper.
• Assignment #13
• • Sullivan Edition 7. Read Chapter 3 Section 5.
  • • Perform each of the following tasks for exercises #28 and 29.
      1. Find the function that represents the sequence of transformations dictated in the problem statement.
      2. Sketch the result on graph paper by hand.
      3. Verify your result with the graphing calculator.
    • Perform each of the following tasks for exercises #40, 47, 50, 55, 57, and 62:
      1. Create a sequence of graphs that lead to the final result, each on a separate coordinate system.
      2. At each stage of the process, state the equation for that stage.
      3. Verify your result with the graphing calculator.
    • Perform each of the following tasks for exercises #65.
      1. Sketch each of the seven requested graphs on graph paper, each on a separate coordinate system.
    • Perform each of the following tasks for exercises #73 and 74:
      1. On graph paper, on a single coordinate system, sketch the original function in blue, then the requested function in red. Use one coordinate system for part(a), a second separate coordinate system for part (b).
  • Sullivan Edition 8. Read Chapter 3, Section 5)
  • • Perform each of the following tasks for exercises #28 and 29.
      1. Find the function that represents the sequence of transformations dictated in the problem statement.
      2. Sketch the result on graph paper by hand.
      3. Verify your result with the graphing calculator.
    • Perform each of the following tasks for exercises #40, 47, 49, 57, 59, and 62:
      1. Create a sequence of graphs that lead to the final result, each on a separate coordinate system.
      2. At each stage of the process, state the equation for that stage.
      3. Verify your result with the graphing calculator.
    • Perform each of the following tasks for exercises #65.
      1. Sketch each of the seven requested graphs on graph paper, each on a separate coordinate system.
    • Perform each of the following tasks for exercises #73 and 74:
      1. On graph paper, on a single coordinate system, sketch the original function in blue, then the requested function in red. Use one coordinate system for part(a), a second separate coordinate system for part (b).
• Prequiz #5, Due Feb. 27, 1:00 PM
• Optimath
• Assignment #14
• • Sullivan Edition 7. Read Chapter 4, Section 1
  • 1. For exercises #28, 31, 32, and 33, perform each of the following tasks.
       • Use the method of completing the square to put each equation in vertex form.
       • Plot and label the vertex and the axis of symmetry.
       • Compute and plot two points on one side of the axis of symmetry, then "mirror" them across the axis of symmetry to plot two "free points."
       • Sketch the parabola and label it with its equation.
    2. For exercises #41, 44, and 51, perform each of the following tasks:
       • Use the shortcut x = -b/2a to help determine the coordinates of the vertex of the parabola. Plot and label the vertex and the axis of symmetry.
       • Calculate and plot the x- and y-intercepts.
       • Graph the parabola and label it with its equation.
    3. For exercises #53 and 58, perform each of the following tasks:
       • Make a copy of the given graph on graph paper.
       • Use the given information to produce the equation of the given parabola. Label the parabola on your graph paper with this equation.
       • Use your graphing calculator to check the result.
    4. For exercise #63 and 66, perform each of the following tasks:
       • Use the x=-b/2a shortcut to determine where the maximum or minimum function value occurs.
       • State the maximum or minimum value of the function.
  • Sullivan Edition 8. Read Chapter 4, Section 3
  • 1. For exercises #28, 31, 32, and 33, perform each of the following tasks.
       • Use the method of completing the square to put each equation in vertex form.
       • Plot and label the vertex and the axis of symmetry.
       • Compute and plot two points on one side of the axis of symmetry, then "mirror" them across the axis of symmetry to plot two "free points."
       • Sketch the parabola and label it with its equation.
    2. For exercises #41, 44, and 51, perform each of the following tasks:
       • Use the shortcut x = -b/2a to help determine the coordinates of the vertex of the parabola. Plot and label the vertex and the axis of symmetry.
       • Calculate and plot the x- and y-intercepts.
       • Graph the parabola and label it with its equation.
    3. For exercises #53 and 58, perform each of the following tasks:
       • Make a copy of the given graph on graph paper.
       • Use the given information to produce the equation of the given parabola. Label the parabola on your graph paper with this equation.
       • Use your graphing calculator to check the result.
    4. For exercise #63 and 66, perform each of the following tasks:
       • Use the x=-b/2a shortcut to determine where the maximum or minimum function value occurs.
       • State the maximum or minimum value of the function.
• Assignment #15
• Sullivan Edition 7. Read Chapter 4, Section 2
• 1. For exercises #59, 60, 66, 67, 68,71, 72, 78, and 80, perform each of the following tasks:
     • Answer each of parts (a)-(f) for each exercise.
     • For each exercise, set up a number line table like that in Table 7 of Example 8 on page 324.
     • Approximate the function near each x-intercept. For example, if f(x)=x(x+2)², as in exercise #60, then near x=0 f is approximated by 4x, and near x=-2, f is approximated by -2(x+2)². Do this as explained in class notes, or refer to Edition 8 of Sullivan for an explanation.
  2. For exercises #85, 90, and 93, perform each of the following tasks:
     • Answer each of parts (a)-(h) for eac exercise.
     • Use your calculator to sketch the given polynomial. Make an accurate copy of the plot on graph paper. Label each axis and indicate the scale on each axis.
• Sullivan Edition 8. Read Chapter 5, Section 1
• 1. For exercises #67, 68, 74, 75, 76, 79, 80, 86, and 88, perform each of the following tasks:
     • Answer each of parts (a)-(f) for eac exercise.
     • For each exercise, set up a number line table like that in Table 3 of Example 6 on page 331.
     • Approximate the function near each x-intercept, as done on pages 332-333 in Example 6, where for example, f is approximated by -2x² near x=0 and f is approximated by 4(x-2) near x=2.
  2. For exercises #89, 94, and 97 perform each of the following tasks:
     • Answer each of parts (a)-(h) for each exercise.
     • Use your calculator to sketch the given polynomial. Make an accurate copy of the plot on graph paper. Label each axis and indicate the scale on each axis.
• Assignment #16
• Sullivan Edition 7. Read Chapter 4, Section 3. There are no exercises assigned in this section, just the reading. Next, read Chapter 4, section 4, then do the following in Chapter 4, Section 4.
• 1. For exercises #7, 10, 11, 14, 15, 17, 18, 37, and 38, perform each of the following tasks:
     • Follow steps 1-7 on page 355 to analyze the graph of the function.
     • Sketch the graph on graph paper. Label each axis and indicate the scale on each axis. Label all asyptotes with their equations and all intercepts with their coordinates.
  2. Follow the directions precisely in exercises #50, 51, and 53. Do all of your work on graph paper.
• Sullivan Edition 8. Read Chapter 5, Section 2. There are no exercises assigned in this section, just the reading. Next, read Chapter 5, section 3, then do the following in Chapter 5, Section 3.
• 1. For exercises #7, 10, 11, 14, 15, 17, 18, 37, and 38, perform each of the following tasks:
     • Follow steps 1-7 on page 355 to analyze the graph of the function.
     • Sketch the graph on graph paper. Label each axis and indicate the scale on each axis. Label all asyptotes with their equations and all intercepts with their coordinates.
  2. Follow the directions precisely in exercises #50, 51, and 53. Do all of your work on graph paper.
• Assignment #17
• Sullivan Edition 7. Read Chapter 4, Section 6.
• 1. Using hand-calculations only (no calculators), answer exercises #21, 29, 45, 46, 55, 56, 63, 65, and 68.
  2. Without the aid of a calculator, sketch the polynomials in exercises #78 and 79. Your computations should include the end-behavior, finding the zeros using the theorems of the section, and behavior of the function near the zeros.
  3. Using only hand-calculations, answer exercises #103, 105, and 107.
• Sullivan Edition 8. Read Chapter 5, Section 5.
• 1. Using hand-calculations only (no calculators), answer exercises #21, 29, 45, 46, 55, 56, 63, 65, and 68.
  2. Without the aid of a calculator, sketch the polynomials in exercises #78 and 79. Your computations should include the end-behavior, finding the zeros using the theorems of the section, and behavior of the function near the zeros.
  3. Using only hand-calculations, answer exercises #103, 105, and 107.
• Assignment #18
• Sullivan Edition 7. Read Chapter 4, Section 7.
• 1. Using hand-calculations only (no calculators), answer exercises #25, 26, 31, 32, 33, 37, and 38.
• Sullivan Edition 8. Read Chapter 5, Section 6.
• 1. Using hand-calculations only (no calculators), answer exercises #25, 26, 31, 32, 33, 37, and 38.
• Assignment #19
• Sullivan Edition 7. Read Chapter 5, Section 1.
• 1. Do exercisdes #7, 35, 40, 48, 51, and 54.
• Sullivan Edition 8. Read Chapter 6, Section 1.
• 1. Do exercises #7, 37, 42, 50, 53, and 56.
• Assignment #20
• Sullivan Edition 7. Read Chapter 5, Section 2.
• 1. For exercises #18 and 19, sketch the given function on graph paper, then apply the horizontal line test and state the result.
  2. For exercises #23 and 25, sketch each graph on graph paper, then sketch the inverse in a different color on the same coordinate system.
  3. Use an algebraic method to show the required result in exercises #32, 33, 34, and 37.
  4. In exercises #42, 43, and 45, use an algebraic method to find the inverse, then sketch the function and its inverse by hand on the same coordinate system. You may not use a calculator to do the work, but you may use your calculator to check your work.
  5. Use an algebraic method to find the inverse of the functions given in exercises #55 and 61.
• Sullivan Edition 8. Read Chapter 6, Section 2.
• 1. For exercises #18 and 19, sketch the given function on graph paper, then apply the horizontal line test and state the result.
  2. For exercises #41 and 43, sketch each graph on graph paper, then sketch the inverse in a different color on the same coordinate system.
  3. Use an algebraic method to show the required result in exercises #34, 35, 36, and 39.
  4. In exercises #50, 51, and 53, use an algebraic method to find the inverse, then sketch the function and its inverse by hand on the same coordinate system. You may not use a calculator to do the work, but you may use your calculator to check your work.
  5. Use an algebraic method to find the inverse of the functions given in exercises #63 and 69.
• Assignment #21
• Sullivan Edition 7. Read Chapter 5, Section 3.
• 1. For exercises #37, 39, 41, 42, 45, 46, 51, and 52, sketch each graph on graph paper. Label the asymptote with its equation and the y-intercept with its coordinates. Describe the domain and range with interval notation.
  2. In exercises #53, 56, 59, 62, 65, 66, 68, and 69, solve the given equation algebraically. Show all of your steps. No credit for answers without an algebraic method.
  3. In exercises #71 and 74, sketch the given graph on graph paper, then start with the general form of the exponential function, namely y = a*b^x and use the data to determine the values of a and b and the equation of the given curve.
  4. Answer each question part posed in exercise #87. Place all of the required responses on graph paper.
  5. Use your calculator to perform the calculations required in exercise #89.
  6. Prove the requested results in exercises #91 and 92.
  7. Answer each part requested in exercises #97 and 98.
• Sullivan Edition 8. Read Chapter 6, Section 3.
• 1. For exercises #37, 43, 47, 48, 49, 50, 55, and 56, sketch each graph on graph paper. Label the asymptote with its equation and the y-intercept with its coordinates. Describe the domain and range with interval notation.
  2. In exercises #63, 66, 68, 69, 70, 71, 75, and 76, solve the given equation algebraically. Show all of your steps. No credit for answers without an algebraic method.
  3. In exercises #87 and 90, sketch the given graph on graph paper, then start with the general form of the exponential function, namely y = a*b^x and use the data to determine the values of a and b and the equation of the given curve.
  4. Answer each question part posed in exercise #107. Place all of the required responses on graph paper.
  5. Use your calculator to perform the calculations required in exercise #109.
  6. Prove the requested results in exercises #111 and 112.
  7. Answer each part requested in exercises #115 and 116.
• Assignment #22
• Sullivan Edition 7. Read Chapter 5, Section 4.
• 1. Do exercises #9, 10, 19, 21, 22, 31, 32, 33-44. Please show your work.
  2. Use an combination of algebra and knowledge of the graph of the logarithmic function to determine the domain of the functions given in exercises #45, 53, 54, 55, and 46. You might want to check your solution by examining the graph on your calculator.
  3. Use your knowledge of transformations (shifting, scaling, reflecting) to sketch the graphs of the functions given in exercises #75, 78, and 82. You should be able to do these without the aid of a calculator, but you should certainly use your calculator to check your work.
  4. Do exercises #91, 94, 98, 99, 101, 104, 105, 111, 114, and 118.
• Sullivan Edition 8. Read Chapter 6, Section 4.
• 1. Do exercises #9, 10, 15, 17, 18, 23, 24, 25-36. Please show your work.
  2. Use an combination of algebra and knowledge of the graph of the logarithmic function to determine the domain of the functions given in exercises #37, 45, 46, 47, and 48. You might want to check your solution by examining the graph on your calculator.
  3. Use your knowledge of transformations (shifting, scaling, reflecting) to sketch the graphs of the functions given in exercises #71, 74, and 76. You should be able to do these without the aid of a calculator, but you should certainly use your calculator to check your work.
  4. Do exercises #87, 90, 94, 95, 97, 100, 101, 117, 120, 124.
• Assignment #23
• Sullivan Edition 7. Read Chapter 5, Section 5.
• 1. Do exercises #8, 9, 13, 16, 17, 19, 22, 25, 28, 29, 39, 40, 41, 43, 51, 52, 62, 63, 65, 72, 74, 75, 81, 84, 94, 95, 96, and 98.
• Sullivan Edition 8. Read Chapter 6, Section 5.
• 1. Do exercises #8, 9, 13, 16, 17, 19, 22, 25, 28, 29, 39, 40, 41, 43, 51, 52, 62, 63, 65, 72, 74, 75, 83, 86, 96, 97, 98, and 100.
• Assignment #24
• Sullivan Edition 7. Read Chapter 5, Section 6.
• 1. Do exercises #1, 4, 6, 7, 13, 20, 21, and 22, using pencil and paper calculations only.
  2. For exercises 9, 12, 29, and 30, perform the following tasks.
     • Solve the given equation algebraically.
     • Use your graphing calculator to find a numerical solution. Copy the resulting graph onto your homework, drop a vertical dashed line throught point(s) of intersection, then shade and label the solution on the x-axis of your plot. Include xmin, xmax, ymin, and ymax on your plot in the usual manner.
  3. Solve exercises #34, 35, 36, 37, and 41 algebraically, using pencil and paper calculations only.
  4. Use a graphing calculator to find numerical solutions for exercises #46 and 51. Copy the resulting plot onto your homework paper, drop a dashed vertical line through point(s) of intersection, then shade and label solutions on the x-axis.
• Sullivan Edition 8. Read Chapter 6, Section 6.
• 1. Do exercises #9, 12, 13, 15, 32, 38, 41, and 42, using pencil and paper calculations only.
  2. For exercises 17, 26, 39, and 40, perform the following tasks.
     • Solve the given equation algebraically.
     • Use your graphing calculator to find a numerical solution. Copy the resulting graph onto your homework, drop a vertical dashed line throught point(s) of intersection, then shade and label the solution on the x-axis of your plot. Include xmin, xmax, ymin, and ymax on your plot in the usual manner.
  3. Solve exercises #30, 61, 75, 77, and 81 algebraically, using pencil and paper calculations only.
  4. Use a graphing calculator to find numerical solutions for exercises #65 and 86. Copy the resulting plot onto your homework paper, drop a dashed vertical line through point(s) of intersection, then shade and label solutions on the x-axis.
• Assignment #25
• Sullivan Edition 7. Read Chapter 5, Section 7.
• 1. Do exercises #3, 4, 11, 15, 18, 21, 31, 34, 40, 45, and 46.
• Sullivan Edition 8. Read Chapter 6, Section 7.
• 1. Do exercises #3, 4, 11, 13, 19, 21, 35, 40, 46, 49, and 50.
• Assignment #26
• Sullivan Edition 7. Read Chapter 5, Section 8.
• 1. Do exercises #1, 3, 5, 9, 13, 15, 19, 21, and 24.
• Sullivan Edition 8. Read Chapter 6, Section 8.
• 1. Do exercises #1, 3, 5, 9, 13, 15, 19, 23, and 26.
• Assignment #27
• Sullivan Edition 7. Read Chapter 11, Section 2.
• 1. Using strictly pencil-and-paper calculations, do each of the following exercises by hand. In each case, set up the augmented matrix, use row operations to place the matrix in row echelon form, then write the resulting system and use back-substitution to solve the system. Exercises #47, 49, 51, 53, 63, 67, 71.
  2. Set up the augmented matrix requested system in exercises #73 on your homework paper. Enter the system into your calculator and put it in reduced row echelon form. Place this result on your homework paper, state the solution. Sketch the resulting parabola on your calculator then verify that the given data points all lie on your parabola.
  3. Set up a system of equations for exercises #79 and 81, then set up the augmented matrix for your system. Place the augmented matrix in your calculator and find the reduced row echelon form of the augmented matrix. Place this result on your homework, then answer the questions posed by the exercise.
• Sullivan Edition 8. Read Chapter 12, Section 2.
• 1. Using strictly pencil-and-paper calculations, do each of the following exercises by hand. In each case, set up the augmented matrix, use row operations to place the matrix in row echelon form, then write the resulting system and use back-substitution to solve the system. Exercises #47, 49, 51, 53, 63, 67, 71.
  2. Set up the augmented matrix requested system in exercises #73 on your homework paper. Enter the system into your calculator and put it in reduced row echelon form. Place this result on your homework paper, state the solution. Sketch the resulting parabola on your calculator then verify that the given data points all lie on your parabola.
  3. Set up a system of equations for exercises #79 and 81, then set up the augmented matrix for your system. Place the augmented matrix in your calculator and find the reduced row echelon form of the augmented matrix. Place this result on your homework, then answer the questions posed by the exercise.
• Assignment #28
• Sullivan Edition 7. Read Chapter 11, Section 3.
• 1. Using strictly pencil-and-paper calculations, do each of the following exercises by hand: #5, 13, 15, 17, 23, 33, 37, 45, 47, 61, 62, 63, and 64.
• Sullivan Edition 8. Read Chapter 12, Section 3.
• 1. Using strictly pencil-and-paper calculations, do each of the following exercises by hand: #5, 13, 15, 17, 23, 33, 37, 45, 47, 62, 63, 64, and 65.
• Assignment #29
• Sullivan Edition 7. Read Chapter 12, Section 1.
• 1. Do exercises #11, 12, 13, and 16. In each case, push the envelope a bit, computing enough terms so you can answer the question "Does the sequence converge or diverge?"
  2. Find an nth term for each of the sequences in exercises #21, 22, 23, and 28.
  3. Write the first five terms of the recursively defined sequences in exercises #30, 37, 38, 39, 40, 41, and 42.
  4. For exercises #44, 47, 49, and 53, perform each of the following tasks:
     • Use Theorem Properties (1)-(8) to determine the sum.
     • Use brute force crunch and grind to find the sum, then compare your answer to the above calculation.
  5. Expand each of the sums in erxercises #59, 62, and 64.
  6. Write each of the sums in exercises #67, 69, 73, in 74 using summation notation.
• Sullivan Edition 8. Read Chapter 13, Section 1.
• 1. Do exercises #17, 18, 19, and 22. In each case, push the envelope a bit, computing enough terms so you can answer the question "Does the sequence converge or diverge?"
  2. Find an nth term for each of the sequences in exercises #27, 28, 39, and 34.
  3. Write the first five terms of the recursively defined sequences in exercises #36, 44, 44, 45, 46, 47, and 48.
  4. For exercises #70, 73, 75, and 80, perform each of the following tasks:
     • Use Theorem Properties (1)-(8) to determine the sum.
     • Use brute force crunch and grind to find the sum, then compare your answer to the above calculation.
  5. Expand each of the sums in erxercises #53, 56, and 58.
  6. Write each of the sums in exercises #61, 63, 67, and 68 using summation notation.
• Assignment #30
• Sullivan Edition 7. Read Chapter 12, Section 2.
• 1. Do exercises #8, 11, 14, 15, 21, 22, 27, 32, 35, 38, 40, and 41.
• Sullivan Edition 8. Read Chapter 13, Section 2.
• 1. Do exercises #8, 11, 14, 15, 21, 22, 27, 32, 35, 38, 40, and 41.
• Assignment #31
• Sullivan Edition 7. Read Chapter 12, Section 3.
• 1. Do exercises #16, 17, 34, 35, 44, 45, 49, 50, 59, 64, 65, and 68.
• Sullivan Edition 8. Read Chapter 13, Section 3.
• 1. Do exercises #16, 17, 34, 35, 44, 48, 63, 64, 67, 72, 75, and 80.
• Assignment #34
• Sullivan Edition 7. Read Chapter 12, Section 5.
• 1. Do exercises #5, 10, 12, 17, 19, 21, 24, 29, 34, 41, 42, 45, and 47.
• Sullivan Edition 8. Read Chapter 13, Section 5.
• 1. Do exercises #5, 10, 12, 17, 19, 21, 24, 29, 34, 41, 42, 45, and 47.

Last Revision: 4/24/09 | Email Webmaster | © Design by Andreas Viklund