the function y = f(x) is graphed below. what ...
the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval -6 ≤ x ≤ 1?
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 $\frac{f(b)-f(a)}{b - a}$. Here, $a=-6$ and $b = 1$.
## Step2: Find $f(-6)$ and $f(1)$ from the graph
From the graph, when $x=-6$, $f(-6)=0$. When $x = 1$, $f(1)=0$.
## Step3: Calculate the average rate of change
Substitute $f(-6)=0$, $f(1)=0$, $a=-6$ and $b = 1$ into the formula: $\frac{f(1)-f(-6)}{1-(-6)}=\frac{0 - 0}{1+6}=0$.
# Answer:
$0$