6:52 PM 7 PQRS * || 76% 8 TUV 9wxyz 0 # = X = -x 3. Sums and Differences of Functions What can be said about the sum and difference of each pair of functions? (a) Two even functions (b) Two odd functions (c) An odd function and an even function 4. Inverse Functions The functions f(x) and g(x) are their own inverse functions. Graph each function and explain why this is true. Graph other linear functions that are their own inverse functions. Find a formula for a family of linear functions that are their own inverse functions. 5. Proof Prove that a function of the form y = 42n2n + a2n–2X2n–2 +...+ a2x2 + ao is an even function. 6. Miniature Golf A golfer is trying to make a hole-in-one on the miniature golf green shown. The golf ball is at the point (2.5, 2) and the hole is at the point (9.5, 2). The golfer wants to bank the ball off the side wall of the green at the point (x, y). Find the coordinates of the point (x, y). Then write an equation for the path of the ball. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copi 76% 6:51 PM 10. Trip Time You are in a boat 2 miles from the nearest point on the coast (see figure). You plan to travel to point Q, 3 miles down the coast and 1 mile inland. You row at 2 miles per hour and walk at 4 miles per hour. 2 mi -X i 1 mi 3 mi > Not drawn to scale (a) Write the total time T (in hours) of the trip as a function of the distance x (in miles). (b) Determine the domain of the function. (c) Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. (d) Find the value of x that minimizes T. (e) Write a brief paragraph interpreting these values. 11. Heaviside Function The Heaviside function H(x) = 1, x > 0 10, x < 0 is widely used in engineering applications. (See figure.) To print an enlarged copy of the graph, go to MathGraphs.com. у cricket TOLLTE vveek Develdvies. 79% | 6:41 PM Problem solving plan (problems found on page 239-240 in textbook) o Problem 6 What parent function does it look like you need to use to fit the shape in Figure 6? § Share your ideas of how you will go about figuring out the equation. There are multiple methods, so if you have more than one idea, share them all! o Problem 10 § In order to find the distance for the red marked paths, does it make more sense to use the Pythagorean Theorem, distance formula, slope, or equation of the line? Could it be possible to use any of them? Explain your answer. S What concept or formula will you need to use in order to create the equation that gives time as a function of distance? Week 6 In week 6 there is no work due. cricket 80% لاال 6:38 PM Х Written Assignment ttps://content.grantham.edu College Algebra - Progressive Project College Algebra Project: Week 7 This week you will complete and submit your final project deliverables. Review the full project details before getting started. Each partner must submit in the W7 Assignment dropbox a Microsoft Word document addressing the following items. The Week 7 Deliverables will be graded using this rubric and will be worth 200 points. Problem 6 o What are the coordinates of the point (x,y)? o Give the equation for the path of the ball, showing all work. Explain why you do each step. o Include a screenshot of the graph of your equation (use Desmos.com), verifying that it goes through the given points. Problem 10 cricket SilualIUIT: JUES LITE value ..l 80% i 6:37 PM 1.L. VIIa uu of x tell us, and what does the value of T tell us? Write a brief paragraph interpreting these values. Reflection on the project as a whole o Process for each problem § Did your idea for solving this work? Did you have to get help or try different methods? § Was this problem easy? Hard? Š Share anything else you have to say about the problems o Working with a partner § Were you and your partner able to communicate well? § What technology did you use to meet and communicate? S How did you split up work? Did that work well? & Share anything else you have to say o Your successes and failures throughout this entire project GRANTHAM COPYRIGHT 2018 UNIVERSITY A 80% الا 6:37 PM cricket . % Problem 6 o What are the coordinates of the point (x,y)? o Give the equation for the path of the ball, showing all work. Explain why you do each step. o Include a screenshot of the graph of your equation (use Desmos.com), verifying that it goes through the given points. Problem 10 o The total time T (in hours) of the trip as a function of the distance x (in miles). Make sure you show all your work to come up with this equation, and explain each step and what it represents. o The domain of the function. Explain why this domain makes sense, and show work as needed. o Graph the function using the graphing utility on Desmos.com. Take a screenshot and make sure it is included in your document. The graph should be focused over the domain of the function. Find the value of x that minimizes cricket Jul 80% 6:37 PM o Find the value of x that minimizes T. Desmos.com will note this ordered pair for you automatically. If it does not, then you can click various points of the graph and it will display the ordered pair. o What does the ordered pair of the minimum for T represent in our situation? I.E. what does the value of x tell us, and what does the value of T tell us? Write a brief paragraph interpreting these values. Reflection on the project as a whole o Process for each problem § Did your idea for solving this work? § Did you have to get help or try different methods? & Was this problem easy? Hard? Š Share anything else you have to say about the problems o Working with a partner & Were you and your partner able to communicate well? Vollmenta منم مصلحضطعم+ +حطا۱۸ cricket SilualIUIT: JUES LITE value ..l 80% i 6:37 PM 1.L. VIIa uu of x tell us, and what does the value of T tell us? Write a brief paragraph interpreting these values. Reflection on the project as a whole o Process for each problem § Did your idea for solving this work? Did you have to get help or try different methods? § Was this problem easy? Hard? Š Share anything else you have to say about the problems o Working with a partner § Were you and your partner able to communicate well? § What technology did you use to meet and communicate? S How did you split up work? Did that work well? & Share anything else you have to say o Your successes and failures throughout this entire project GRANTHAM COPYRIGHT 2018 UNIVERSITY A