Question

the graph of a function g is shown below. use the graph of the function to find its average rate of change from x = 1 to x = 4. simplify your answer as much as possible.

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = g(x)$ from $x=a$ to $x = b$ is $\frac{g(b)-g(a)}{b - a}$. Here, $a = 1$, $b = 4$.

Step2: Determine $g(1)$ and $g(4)$ from the graph

From the graph, when $x = 1$, $g(1)=4$; when $x = 4$, $g(4)=16$.

Step3: Calculate the average rate of change

Substitute $g(1)=4$, $g(4)=16$, $a = 1$, and $b = 4$ into the formula: $\frac{g(4)-g(1)}{4 - 1}=\frac{16 - 4}{3}$.

Step4: Simplify the expression

$\frac{16 - 4}{3}=\frac{12}{3}=4$.

Answer:

$4$