Question

hich function is shown in the graph?

A function that consists of two connected rays. The left ray passes through the point negative 4 comma 2 and decreases to the origin. The second ray starts at the origin and increases through the point 1 comma 1.
A. f(x) = |x|
B. f(x) = 12
|x|
C. f(x) = {−12x,ifx≤0x,ifx>0
D. f(x) = {12x,ifx≤0x,ifx>0
Part B
For the function in Part A, what is the average rate of change over the interval −3 < x < −1? Give your answer to one decimal place if necessary.

average rate of change =

Answer 1

Part A: C — the graph is f(x) = { −(1/2)x for x ≤ 0; x for x > 0 }.

Part B: Average rate of change on [−3, −1] = (f(−1) − f(−3))/(−1 − (−3))
= (0.5 − 1.5)/2 = −1/2 = −0.5.