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 -4 ≤ x ≤ -3?
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, $a=-4$ and $b = - 3$.
Step2: Read function values from the graph
From the graph, when $x=-4$, $f(-4)=0$; when $x=-3$, $f(-3)=40$.
Step3: Calculate the average rate of change
Substitute $a=-4$, $b=-3$, $f(-4)=0$, and $f(-3)=40$ into the formula: $\frac{f(-3)-f(-4)}{-3-(-4)}=\frac{40 - 0}{-3 + 4}$. $\frac{40-0}{-3 + 4}=\frac{40}{1}=40$.
Answer:
40