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13 Mar 2018

5. (a) (5 points) The figure below shows graphs of two exponential functions. Match each of the following two functions to a graph. (1) f(x) = 2* : Graph (I or II) (2) g(x) - 3*: Graph_ (I or II) 7 05 15 2.5 35 45 (b) (15 points) Given f(x), g(x), h(x) below. X 0112T 3T 4 f(x) 10 13 16 19 22 g(x) 4 8 11 9 6 | h(x) 2 3 4.5 6.75 10.125 (1) (5 pts) Determine which function could represent an exponential function. Show your reason. (2) (10 pts) Find the explicit formula for the exponential function.

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Nelly Stracke
Nelly StrackeLv2
13 Mar 2018
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1. (25 pts) The graph of a function f is given in the figure below. The domain of fis (-, +.). Use the graph of fto answer the questions below. yax) y=f(x) -3 - 2 3 4 (I) (1 pt) Find the range of f. (II) Find the following values. (Note: Possible answers include + , -, or "does not exist".) (a) (1 pt) (x) = 5 (b) (1 pt) lim f (x) = 5 (0) (1 pt) Tim f (x) = 5 (d) (1 pt) f(3) = 2 (e) (2 pts) lim f (x) = + 0 x-2- (8) (2 pts) 11m = (x) = 0 (g) (2 pts) lim f (x) = DOES NOT EXIST x+-2 (h) (2 pts) Lim f (x) = 0 (i) (2 pts) lim f (x) = + X +00 (III) (2 pts) Find all vertical asymptotes. x = -2 (IV) (2 pts) Find all horizontal asymptotes. y = 0 (v) (2 pts) Find all slant asymptotes. | y = x + 2 (VI) (4 pts) Determine the intervals of continuity for f. (-00, -2), [-2, 3), and (3, +c)

1. (25 pts) The graph of a function fis given in the figure below. The domain of fis (-, +.). Use the graph of fto answer the questions below. y = f(x) y=f(x) -3 -1 1 2 3 4 (I) (1 pt) Find the range of f. Range of f = (II) Find the following values. (Note: Possible answers include + , -, or "does not exist".) (a) (1 pt) lim f (x) = x+3+ (b) (1 pt) lim f (x) = (C) (1 pt) lim f (x) = x+3 (a) (1 pt) f(3) = (e) (2 pts) lim f (x) = (f) (2 pts) lim f(x) = (g) (2 pts) lim f (x) = (h) (2 pts) lim f (x) = (i) (2 pts) lim f (x) = (III) (2 pts) Find all vertical asymptotes. (IV) (2 pts) Find all horizontal asymptotes. (V) (2 pts) Find all slant asymptotes. (VI) (4 pts) Determine the intervals of continuity for f.

4. (16 pts) MULTIPLE CHOICE! CIRCLE THE CORRECT ANSWER IN EACH PART. (I) ( 4 pts) Complete the statement of the Intermediate Value Theorem: Suppose f is continuous on the interval [a, b] and L is a number between f (a) and f (b). Then there is at least one number c in (a, b) such that (a) C = L; (b) f(c) = 0; (c) f(c) = L; (a) f' (c) = L; (e) C = 0; (f) f (a) < c < f (b); (g) NONE OF THE PREVIOUS ANSWERS. (II) (4 pts) The figure shows the graph of a function f. At what point (points) c does the conclusion of the Intermediate Value Theorem hold for f (x) on the interval [1, 5] and L = 2. --- - - - -1 - - - 2 - - I- - - (a) c = 1; (b) C = 0; (c) C = 2; (a) c = 3; (e) C = 4; (f) C = 5; (g) c= -1. (III) (4 pts) Given that cos x s f (x) s et, for all x > 0 evaluate lim f (x) x+0+ (a) lim f (x) = 0; (b) lim f (x) = 1; (c) lim f (x) = e; x0+ X0+ (d) lim f(x) DOES NOT EXIST. WE DON'T HAVE ENOUGH INFORMATION TO ANSWER THE QUESTION *40+ (IV) (4 pts) Given the function 1 f (x) = , find its inverse, f+(x) x -2 (a) f (x) = x -2; (b) fΒ«+ (x) = x+2 ; (c) fΒΊ+ (x) = -2; (f) f-+ (x) -2; (e) f (x) DOES NOT EXIST.

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