Determine which graph is the graph of f(x) if the following are true. = 0. f(x) has a horizontal asymptote at y = f'(x) is positive on (-∞, -3). f'(x) is negative on (-3, ∞). . f"(x) is positive on (-∞, -3) u (-3, ∞). f"(x) is negative nowhere. O -15 -10 -5 y 15 10 10 -5 -10 15 5 10 15 -15 -10 -5 a 15- 10 5 -5 -10- |--15 5 10 15 x

Determine which graph is the graph of f(x) if the following are true. • f(x) has a horizontal asymptote at y = 0. . f(x) is positive on (-, -4). . . f(x) is negative on (-4, ∞). f(x) is positive on (-, -4) U (-4, w). "(x) is negative nowhere. 15 y 10 5 x -15 -10 13 10 15 -15 10 5 10- 10 5 10- 15 00 15H x 5 10 15' -15 -10 15 10 5 5 10 15 y x S 15 -15 10 -S y 15 10 5 5 10 15h S 10 15

#10) find the indicated quantity for y=f(x)=5-x^2 and interpret that quantity in terms of the following graph.

1. (a) For the function f(x)=x* - x² (whose %3| | graph is shown) use the power rule to take derivatives and find f'(x), f"(x) and f"(x). -5- -5 (b) Graph all four functions together on a graphing utility (like Desmos) and then sketch all the functions --5- on the same axes at right. Make sure that horizontal tangents of each function line up with x-intercepts of its derivative (that's what l'll be checking for).

1/4 - -3/4 -π/2/4 6+ 5 4 3 2 1 -1 -2- -3 -5 -6+ π/4 T/2 3/4 Identify the function whose graph appears above. f(x) = R 5T/.

☐ 1. The figure below shows the graphs of f(x), f'(x), and f" (x). Identify each curve. orange black blue -2- W --2 Choices f(x) f'(x) f"(x) ☐ 2. The figure below shows the graphs of f(x), f'(x), and f" (x). Identify each curve. orange blue black №- 0 --2 N- Choices f(x) f'(x) f" (x)

Use the given information to sketch the graph of f. Domain: All real x, except x = -4 and x = 4. f(-6)= -3; f(0) = 0; f(6) = 3. f'(x) 0 on (-4, 4). f''(x) 0 on (0, 4) and (4, ∞). Vertical asymptotes: x= -4 and x = 4; Horizontal asymptote: y = 0.

T Z. Al (a) The graph of f(x) = ( + 42) can be obtained from shifting the graph of f(x) = to the 42 units. (b) The graph of f(x) = x + 42 can be obtained from shifting the graph of f(x) = 1 42 units. the graph of f(x) = VT (c) The graph of f(r) = 42,/ can be obtained from vertically by a factor 42. (d) The graph of f(x) = V42x can be obtained from the graph of f(x) = VT 1. horizontally by a factor 42 For each question, enter one of: left, right, upward, downward, stretching, shrinking > Next Question 30 MacBook Air F1 DOO F4 F2 F3 F5 24 4 23 & 2 6. tab R. caps lock shift