the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the…

Answer:

-2.5

Explanation:

Step1: Define the average rate of change formula.

The average rate of change of a function $f(x)$ over the interval $[a, b]$ is given by $\frac{f(b) - f(a)}{b - a}$.

Step2: Identify the interval endpoints.

The given interval is $5 \le x \le 7$, so $a = 5$ and $b = 7$.

Step3: Find the function values from the graph.

From the graph, find the $y$-values corresponding to $x=5$ and $x=7$. When $x = 5$, $y = f(5) = 15$. When $x = 7$, $y = f(7) = 10$.

Step4: Substitute the values into the formula.

Substitute $a=5$, $b=7$, $f(5)=15$, and $f(7)=10$ into the formula. $$ \text{Average Rate of Change} = \frac{f(7) - f(5)}{7 - 5} = \frac{10 - 15}{7 - 5} $$

Step5: Calculate the average rate of change.

Simplify the expression. $$ \text{Average Rate of Change} = \frac{-5}{2} = -2.5 $$