the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the…
the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval -7 ≤ x ≤ -5?
Answer
Explanation:
Step1: Recall average - rate - of - change formula
The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a=-7$ and $b = - 5$.
Step2: Find $f(-7)$ and $f(-5)$ from the graph
From the graph, when $x=-7$, $f(-7)=4$. When $x = - 5$, $f(-5)=12$.
Step3: Calculate the average rate of change
Substitute $a=-7$, $b=-5$, $f(-7)=4$, and $f(-5)=12$ into the formula: $\frac{f(-5)-f(-7)}{-5-(-7)}=\frac{12 - 4}{-5 + 7}=\frac{8}{2}=4$.
Answer:
4