Q. 25 - Precalculus Enhanced with Graphing Utilities

Question

Find the average rate of change from $2$ to $3$ for each function $f$. Be sure to simplify.

$f\left(x\right)=2-5x$

Step-by-Step Solution

Answer

The average rate of change is $-5$.

Step 1. Find f ( 2 ) and f ( 3 )

Consider the function$f\left(x\right)=2-5x$.

Now the function value for $x=2$ is given as

$$\begin{gathered} f\left(2\right)=2-5\times 2 \\ f\left(2\right)=2-10 \\ f\left(2\right)=-8 \end{gathered}$$

Again, the function value for $x=3$ is given as

$$\begin{gathered} f\left(3\right)=2-5\times 3 \\ f\left(3\right)=2-15 \\ f\left(3\right)=-13 \end{gathered}$$

Step 2. Find the average rate of change

The average of change for the function $f\left(x\right)$ from $2$ to $3$ is given as

$\begin{array}{rcl}\frac{f\left(3\right)-f\left(2\right)}{3-2}& =& \frac{-13-(-8)}{1}\\ & =& -13+8\\ & =& -5\end{array}$