Question

The function

y
=
f
(
x
)
y=f(x) is graphed below. Plot a line segment connecting the points on
f
f where
x
=
−
4
x=−4 and
x
=
1.
x=1. Use the line segment to determine the average rate of change of the function
f
(
x
)
f(x) on the interval
−
4
≤
x
≤
1.
−4≤x≤1.

Answer 1

To calculate the average rate of change of the function f ( x ) f(x) on the interval − 4 ≤ x ≤ 1. −4≤x≤1, you need to find the slope of the line segment connecting the points (− 4 , f ( − 4 ) ) (x1, y1) and ( 1 , f ( 1 ) ) (x2, y2). The slope of the line is equal to the change in y divided by the change in x.

The change in y is equal to f ( 1 ) − f ( − 4 ) f(1) - f(-4). The change in x is equal to 1 − ( − 4 ) = 5. 1-(-4) = 5.

Therefore, the slope of the line segment connecting the two points is f ( 1 ) − f ( − 4 ) 5 f(1) - f(-4)/5, which is equal to the average rate of change of the function f ( x ) f(x) on the interval − 4 ≤ x ≤ 1. −4≤x≤1.