x+5)(x-2)2 (x-3) Select the Domain of the rational function R(x) a. (-00, -5) U (-5,2) U (2,3) U (3, 0) b. (-∞, 2) U (2,3) U (3, 0) C. (-00, 3) U (3, 0)

Let f ( x ) = x^ 2 − 1 and g ( x ) = 3 x. Find ( f ∘ g ) ( x ). group of answers 3x^3 − 3x 3 x^2 − 3 9x^2 − 1 3x^2- 1

Given the domain of f(x) is (-∞, 0) and the graph of f "(x) is shown below, find where f(x) is concave up. y f"(x) -6 5 -4 -3 -2 -I 0 1 2 3 4 5 6

The function f(x) has a domain of [-9, 9] and is plotted below such that the portion of the graph on the interval (-2, 1) is hidden from view. Given that f(-2) = −3 and f(1) = 5, determine what conclusions can be drawn based on the Intermediate Value Theorem on the interval (-2, 1). -10-9-8-7 -6 -5 -4 -3 -2 Since the function f(x) is | Intermediate Value Theorem y ? ? ? ? ? ? r I r 1 I L I L I I 2 19 3 Graph of f 4 5 6 7 8 9 10 X ✓on its domain, the

(0, 2) Given the graph of f (x) (-3, 0) (3, 0) -4 2 4 |(-2, 0) (1, 0)

Let fx)=1+x+x² and h = 0. (a) Does f(5+1)=f(5) + 1)? Yes .No Well done! (b) Find fx + h). (c) Does f(x+h)-f(x) + f(h)? O Yes No Great! (d) Does f(x+h)-f(x) +h? O Yes No You're right! (e) Find f(x+h)-, -1x) h and simplify

Let f(x) Then (f o g)(x) — — 2* — 5x – 4 and g(x) 4x + 2. = x - - (g o f)(x)

5. Find the x- and y- intercepts of the rational function : f(x) = (a) (6, 0),(0,2) (b) (6,0) ,(0,-2) (c) (3, 0) ,(0,-2) (d) (-2, 0), (6,0)

x² + 1 f(x) = (x – 4)(x + 7) Complete the statement As x → 4+,f(x) → ..

of of Let f(x,y) = 4x2 + 4xy-3y2 + 7x-7y-2. Find (2, ,-4) and (2,- 4). of (2,- 4) =(Simplify your answer.) of (2, - 4) =(Simplify your answer.) Enter your answer in each of the answer boxes.