Question

the graph of a function f is shown below. use the graph of the function to find its average rate of change from x=0 to x=4. simplify your answer as much as possible.

Explanation:

Step1: Identify f(0) and f(4)

From the graph, $f(0)=1$ and $f(4)=16$.

Step2: Apply average rate formula

The average rate of change is $\frac{f(b)-f(a)}{b-a}$ for $a=0$, $b=4$.
$\text{Average rate of change} = \frac{f(4)-f(0)}{4-0} = \frac{16-1}{4-0}$

Step3: Simplify the expression

$\frac{16-1}{4-0} = \frac{15}{4}$

Answer:

$\frac{15}{4}$