GJ Homework 2 - Coderunner Homework Help - Q&A from On X HW.3.pdf C File | C:/Users/zgher/Downloads/HW%203.pdf O Z Paused HW 3.pdf 2 / 4 - 75% + 2. Consider the functions f(x) = x2 -4, g(2) = h(x ) = Vx + 4. Compute the following compositions and state their domains. (a) (fog)(x) (b) (go f) (x) (c) (foh)(x) (d) (hof)(x) 3. Find f(x) and g(x) such that f(9(x)) = 4x2 + 4x + 1 and g(x) is a linear expression of the form mx + b. 4. Let R(p) be the number of completed rides for a ride-booking service during each hour when the price is p dollars per mile. (a) What does the expression R(2.25) represent? (b) The ride-booking service completes n rides when they charge an average price in the area of po dollars per mile. Therefore, we get the equation R(po) = n. Explain the meaning of the following expressions: i. R(2.5po) ii. 2R(po) iii. R(Po + 0.50) iv. R(po) + 2 (c) Explain why we can multiply and add decimals/fractions to po, but we cannot multiply Type here to search o 3:20 PM Rain... 9/14/2023GJ Homework 2 - Coderunner Homework Help - Q&A from On X HW.3.pdf C File | C:/Users/zgher/Downloads/HW%203.pdf O Z Paused HW 3.pdf 3 / 4 - 75% + (c) Explain why we can multiply and add decimals/fractions to po, but we cannot multiply or add decimals/fractions to R(Po). (d) The ride-booking service has decided to implement dynamic pricing so that p would depend on the time of day t. That is, p(t) is the price (in dollars per mile) at time t. Explain how we can use composition of functions to model the ride-booking service's new policy for the number of completed rides. 2 University of Colorado-Boulder MATH 1150 Homework 3 5. Fill in the blank with "all", "no", or "some" to make the following statements true. Note that "some" means one or more instances, but not all. . If your answer is "all", then give a brief explanation as to why. . If your answer is "no", then give an example and a brief explanation as to why. . If your answer is "some", then give two specific examples that illustrate why your answer it not "all" or "no". Be sure to explain your two examples. An example must include either a graph or a specific function. (a) For functions f and g, f(g(x)) = 9(f(x)). (b) For values of x in the interval (-co, co), if f(x) = x2 and g(x) = vx + 2, then f(g(x) ) = x+2. In mathematics. we consider a statement to be false if we can find any examples where Type here to search o XJ 3:20 PM Rain... 9/14/2023In matheumt' -. we consider it statement to be false if we can nd any exmnples where the statement is not true. We refer to these examples as counterexamples. Note that e counterexample- is an ex uple for which [In-- "if" part of the etetement is true, hut the \"their" part of the statement is false. . Patrick. a fellow Precalculus enthusiast. was asked to write down a formula for the function g obtained by performing the following sequence of transformations on [(a:) : 1 Shift right by 2 units, then shift up by 5 units, and then stretch vertically by a factor of 3. \"(1-) = +5, but a tutor in the MARC told him his answer is not chi-rent. 1) did Patrick make. and what is the correct answer? 3:21 PM X ,0 Type here to search a 9/14/2023 5 GJ Homework 2 - Coderunner Homework Help - Q&A from On X HW.3.pdf C File | C:/Users/zgher/Downloads/HW%203.pdf O Z Paused HW 3.pdf 4 / 4 75% + 7. Use the graph of the function k(x) to answer the following problems. y = k(x) -5-4-3 2-1 1 2 3 4 5 (a) Graph the following transformations of k(x). Be sure to explain the reasoning for your graphs. (i) f(x) = k(-2x + 1) (ii) g(x) = -2k(x) + 1 (b) Find a formula for the following transformation of k(x). By "formula," we mean an expression in the form of those given in part (a). Be sure to explain the reasoning for your formula. No do -5-4-3-2 - 1 2 3 4 5 Type here to search Co O 66.F 3:21 PM 9/14/2023GJ Homework 2 - Coderunner Homework Help - Q&A from On X HW.3.pdf C File | C:/Users/zgher/Downloads/HW%203.pdf O Z Paused HW 3.pdf 4 / 4 75% + -5 -4 -3 2- 1 2 3 4 5 -5 (a) Graph the following transformations of k(x). Be sure to explain the reasoning for your graphs. (i) f(x) = k(-2x + 1) (ii) g(x) = -2k(x) + 1 (b) Find a formula for the following transformation of k(x). By "formula," we mean an expression in the form of those given in part (a). Be sure to explain the reasoning for your formula. -5-4-3-2-4 1 2 3 4 5 -21 4 Type here to search V 3:21 PM 66.F 9/14/2023University of ColoradoBouldcr MATH 1150 Homework 3 Turn in the following problems: 1. Use the graph of the function f end for-mule of the function g to to answer the following problems. If a function is not dened at a point, he sure to explain why. Be sure to show all your work, y:f(x) (a) Given ll,('r,) : y(f(.r)). evaluate m). (b) Given C(I) : mm), evaluate c(2). (c) Given l(a:) =f(f(1)). evaluate 1(2). (d) Given d(r) : f((f(.1:))2). evaluate 4(2). 3:20 PM a 9/14/2023 ,0 Type here to search