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Exercises Functions

Example 2 from Algebra and Trigonometry, 3.3 Rates of Change and Behavior of Graphs

Computing Average Rate of Change from a Graph

Given the function $g (2) = 1.$ shown in Figure 1, find the average rate of change on the interval $[- 1, 2] .$

Graph of a parabola.

Figure 1

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
At $t = - 1,$ Figure 2 shows $g (−1) = 4.$ At $t = 2,$ the graph shows $g (2) = 1.$

Figure 2

The horizontal change $Δ t = 3$ is shown by the red arrow, and the vertical change $Δ g (t) = - 3$ is shown by the turquoise arrow. The average rate of change is shown by the slope of the orange line segment. The output changes by –3 while the input changes by 3, giving an average rate of change of
$\frac{1 - 4}{2 - (- 1)} = \frac{- 3}{3} = −1$

How did it go?

PreviousComputing an Average Rate of Change Next Computing Average Rate of Change from a Table

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 3.3, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.