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 = 3. simplify your answer as much as possible.

Explanation:

Step1: Identify f(0) from graph

From the graph, when $x=0$, $f(0)=3$.

Step2: Identify f(3) from graph

From the graph, when $x=3$, $f(3)=10$.

Step3: Apply average rate formula

The average rate of change formula is $\frac{f(b)-f(a)}{b-a}$ for interval $[a,b]$. Here $a=0$, $b=3$.
$\text{Average rate} = \frac{f(3)-f(0)}{3-0} = \frac{10-3}{3-0}$

Step4: Simplify the expression

$\frac{10-3}{3-0} = \frac{7}{3}$

Answer:

$\frac{7}{3}$