Section 1.2 Enhanced Assignment

Instructor: Neelam Aggarwal Course: Spring 2022 - Calculus I (MATH1441-02F) Student: Jalen Wilson Date: 07/11/24 1. For the given​functions, find the domains and ranges of​f, g, and f + ​g, and find f • g. ​f(x) = x + 5 ​, ​g(x) = x−8 Find the domain of f. [ − 5,∞) ​(Type your answer in interval​notation.) Find the range of f. [0,∞) ​(Type your answer in interval​notation.) Find the domain of g. [8,∞) ​(Type your answer in interval​notation.) Find the range of g. [0,∞) ​(Type your answer in interval​notation.) Find the domain of f + g. [8,∞) ​(Type your answer in interval​notation.) Find the range of f + g. 13 ,∞ ​(Type your answer in interval​notation.) Find the domain of f • g. [8,∞) ​(Type your answer in interval​notation.) Find the range of f • g. [0,∞) ​(Type your answer in interval​notation.) Assignment: Section 1.2 Enhanced Assignment 2. 2 For ​f(x) = 6 and ​g(x) = 2x + 1​, find the domains and ranges of​f, g, f g ​, and g f . Select the correct choice for the domain of f below and fill in the answer box to complete your choice. A. The domain is an interval. The domain is ( − ∞, ∞) . ​(Type your answer in interval​notation.) B. The domain is a list of values. The domain is ​{ ​(Use a comma to separate answers as​needed.) ​}. Select the correct choice for the range of f below and fill in the answer box to complete your choice. A. The range is a list of values. The range is ​{ 6 ​(Use a comma to separate answers as​needed.) B. The range is an interval. The range is ​(Type your answer in interval​notation.) ​}. . Select the correct choice for the domain of g below and fill in the answer box to complete your choice. A. The domain is an interval. The domain is ( − ∞, ∞) . ​(Type your answer in interval​notation.) B. The domain is a list of values. The domain is ​{ ​(Use a comma to separate answers as​needed.) ​}. Select the correct choice for the range of g below and fill in the answer box to complete your choice. [1,∞) A. The range is an interval. The range is . ​(Type your answer in interval​notation.) B. The range is a list of values. The range is ​{ ​(Use a comma to separate answers as​needed.) Select the correct choice for the domain of f g ​}. below and fill in the answer box to complete your choice. A. The domain is an interval. The domain is ( − ∞, ∞) . ​(Type your answer in interval​notation.) B. The domain is a list of values. The domain is ​{ ​(Use a comma to separate answers as​needed.) Select the correct choice for the range of f g ​}. below and fill in the answer box to complete your choice. A. The range is a list of values. The range is ​{ ​}. ​(Use a comma to separate answers as​needed.) B. The range is an interval. The range is (0,6] . ​(Type your answer in interval​notation.) Select the correct choice for the domain of g f below and fill in the answer box to complete your choice. A. The domain is a list of values. The domain is ​{ ​(Use a comma to separate answers as​needed.) B. The domain is an interval. The domain is ( − ∞, ∞) ​}. . ​(Type your answer in interval​notation.) Select the correct choice for the range of g f below and fill in the answer box to complete your choice. A. The range is an interval. The range is 1 6 ,∞ . (Type your answer in interval​notation.) B. The range is a list of values. The range is ​{ (Use a comma to separate answers as​needed.) 3. If f(x) = x + 3 and ​g(x) = x2 − 2​, find the following. a.​f(g(0)) b.​g(f(0)) c. ​f(g(x)) d.​g(f(x)) e.​f(f( − 6​)) f.​g(g(3​)) g.​f(f(x)) h.​g(g(x)) a. ​f(g(0)) = 1 ​(Simplify your​answer.) b. ​g(f(0)) = 7 ​(Simplify your​answer.) 2 c. ​f(g(x)) = x +1 ​(Simplify your​answer.) d. ​g(f(x)) = 2 x + 6x + 7 ​(Simplify your​answer.) e. ​f(f( − 6​)) = 0 ​(Simplify your​answer.) f. ​g(g(3​)) = 47 ​(Simplify your​answer.) g. ​f(f(x)) = x+6 ​(Simplify your​answer.) h. ​g(g(x)) = 4 2 x − 4x + 2 ​(Simplify your​answer.) ​}. 4. Graph the equations listed in parts ​(a) to ​(d). 2 2 ​(a) y = (x − 2) − 4 ​(b) y = (x − 2) + 3 2 2 ​(c) y = (x + 1) + 1 ​(d) y = (x + 3) − 2 2 ​(a) Which of the following gives the correct graph of y = (x − 2) − 4​? A. B. 8 y C. 8 y 8 x -8 8 D. y 8 x -8 -8 8 y x -8 -8 8 x -8 -8 8 -8 2 ​(b) Which of the following gives the correct graph of y = (x − 2) + 3​? A. B. 10 y C. 10 y x -10 10 D. 10 y x -10 -10 10 10 y x -10 -10 10 x -10 -10 10 -10 2 ​(c) Which of the following gives the correct graph of y = (x + 1) + 1​? A. B. 10 y C. 10 y x -10 10 D. 10 y x -10 -10 10 10 y x -10 -10 10 x -10 -10 10 -10 2 ​(d) Which of the following gives the correct graph of y = (x + 3) − 2​? A. B. 10 y C. 10 x -10 10 -10 y D. 10 x -10 10 -10 y 10 x -10 10 -10 y x -10 10 -10 5. The number of units and the direction that the given function is to be shifted are given. Give an equation for the shifted graph. Then sketch the original and shifted graphs​together, labeling each graph with its equation. y=x 3 Left 5​, Down 5 3 The equation for the shifted graph is y = (x + 5) − 5 . Sketch the original and shifted graphs​together, labeling each graph with its equation. A. B. 10 y 3 y=x C. 10 y D. 10 y 3 y=x 10 3 3 y= −x x -10 10 x -10 -10 3 y = (x + 5) − 5 10 y=x x -10 y=x−5 3 y=x -10 y 10 x -10 -10 3 y = (x + 5) + 5 10 -10 6. Graph the function y = x + 2 . 10 8 6 4 2 Use the graphing tool to graph the function. -10 -8 -6 -4 -2-2 -4 -6 -8 -10 y x 2 4 6 8 10 2 7. Let ​f(x) = 3x − 1 and ​g(x) = x − 2. Find ​f(g(6​)). ​f(g(6​)) = 101 8. Graph the following function. y= 1 x−4 Choose the correct graph below. A. B. 12 y C. 12 x -12 12 -12 y D. 12 x -12 12 -12 y 12 x -12 12 -12 y x -12 12 -12 9. Graph the following function. y= 1 x +9 Choose the correct graph below. A. B. 16 C. y 16 y x -16 16 D. 16 y x -16 16 -16 -16 16 x -16 16 3 3 Which transformations will be used to transform the graph of y = x to the given​function? Select all that apply. -10 -8 -6 -4 -2-2 -4 -6 -8 -10 B. Horizontal shift C. Reflection across the​y-axis D. Horizontal​stretch/compression E. Vertical shift F. Reflection across the​x-axis Use the graphing tool to graph the function. 11. For the given​functions, find ​(f ◦ ​g)(x) and ​(g ◦ ​f)(x) and the domain of each. x 2 x +1 ​(g ◦ ​f)(x) = 2x + 1 The domain of f ◦ g is The domain of g ◦ f is 0 − ​(Type an integer or a​fraction.) 1 2 16 10 8 6 4 2 y = ​(4 − ​x) + 6 ​(f ◦ ​g)(x) = -16 -16 10. Graph the following function by starting with the graph of y = x3 and applying an appropriate transformation. ​f(x) = 2x + 1​, ​g(x) = x -16 A. Vertical​stretch/compression ,∞ . ,∞ . y y x 2 4 6 8 10 12. Determine the amplitude and phase shift of the following function. Also choose its graph. y = sin x + π 2 The amplitude is 1 The phase shift is − . π 2 . Choose the correct graph. A. B. 5 y C. 5 y 5 x -5 5 -5 D. y -5 x -5 5 -5 0 x -5 5 -5 -10 y x 5