The graph of f is shown for the interval [-2, 6]. 45 40 35 30 25 20 15 10 5 0 54 y x' -3 -2 -1 0 1 2 3 4 5 6 7 8 For which interval is f' < 0 and f" > 0? ○ (-2,0) ○ (0,2) ○ (2,4) ○ (4,6)

How do the graphs of the functions f(x)=x2 and f(x)=x21 differ? We graphed them at the start of this section. What is the difference between their graphs? How are their graphs the same?

Describe all numbers x that are at a distance of 12 from the number - 4. Express this using absolute value notation.

Use a graphing utility to graph f(x)=10|x-|2 on the viewing window [0,4] . Identify the corresponding range. Show the graph.

(-2,2), Consider graph on the left side, de- termine if the function f(x) is continu- ous on the following intervals: (0.1) (3,0), * 1) (-1,2) -3 -2 4. (-2. -1) (3.-1) 2) [0, 3] 3) (-4, -1) 4) (-2,3)

The graph of f is shown below. 10 (-2, 7.333) (0, 0) (5.058, 0) 4 2 4 (-3.558, 0) --10 (3, -13.5) Complete the following statements. f'(x) > 0 on the interval(s) f' (x) 0 on the interval(s) f" (x) < 0 on the interval(s)

Graph function

Find the slope of the graph of the function at the given value. f(x)=-4x²+6x- when x=-3 O a) f(-3)= 802 9 802 b) f(-3)=-- 27 802 27 c) f(-3)=- d) f'(-3)=- e) f(-3)= 802 802 3

For the function whose graph is shown below, at which value of x is the graph continuous and differentiable? (2,5) -5- (-2,0) -5 |(2, 4)– 0 --5- --10- (3,0) 5

The one-to-one functions g and h are defined as follows. g={(-5, 8), (2, −7), (7, 4), (9, 7)} h(x)=3x+14 Find the following. -1 9 (7) = ] -1 11(x) = 0 -(9-)("..-") =