Rates of Change and Behavior of Graphs · Exercise 4

Find the slope of a line and the average rate of change.

ⓐ Complete the following table of values for $g\left(x\right)=\frac{1}{x+3}$

$$\begin{array}{cc}\text{x}& \text{g(x)}\\ \text{–1}& \\ \text{0}& \\ \text{2}& \end{array}$$
ⓑ Use the table above to find the average rate of change between x=–1 and x=0.
ⓒ Use the table above to find the average rate of change between x=–1 and x=2.
ⓓ Sketch the graph of g(x) below and graph the lines with slopes equal to the average rates of change found in parts ⓑ and ⓒ.

This problem refers to a figure in its source book that isn't reproduced here.

OpenStax, Algebra and Trigonometry 2e · §3.3 Rates of Change and Behavior of Graphs · Exercise 4