Question

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

Answer 1

The line connecting the points on the graph is shown below:

From it we notice that to get to the first point of the lineto the second we need to:

• Move down 6 squares; since each square has a length of 2 units this means that we move 12 units down.

,

• Move 5 units to the right.

Therefore, we have that:

$\begin{gathered} \Delta y=-12 \\ \Delta x=5 \end{gathered}$

and that:

$\text{ average rate of change=-}\frac{12}{5}$