Question

Find the average rate of change for f(x) = x2 + 9x + 18 from x = −8 to x = −2.

A)−1
B)−3
C)1
D)3

Answer 1

In order to find the average rate of change, we must take the values at x=-8 and x= -2, and determine what the slope would be if a line was drawn between the two points.
f(-8) = -8² +9(-8) + 18
f(-8) = 10

f(-2) = -2² + 9(-2) + 18
f(-2) =4 -18 +18
f(-2) = 4

f(-8) =10 and f(-2)=4

if a line was drawn between the two points (-8,10) and (-2,4) the slope (rise/run) would be -6/6, since the line would go down 6 units from 10 to 4, and over 6 units from x=-8 to x=-2.

The average rate of change, therefore, is -6/6, or
A)-1