Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $2 \leq x \leq 7$?

Explanation:

Step1: Identify f(2) and f(7)

From the graph: $f(2) = -5$, $f(7) = 40$

Step2: Apply average rate formula

The formula for average rate of change on $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$. Substitute $a=2$, $b=7$:
$\frac{f(7)-f(2)}{7-2} = \frac{40 - (-5)}{7-2}$

Step3: Calculate the result

Simplify numerator and denominator:
$\frac{40 + 5}{5} = \frac{45}{5} = 9$

Answer:

9