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 $-5leq xleq3$?
Answer
Explanation:
Step1: Recall the 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=-5) and (b = 3).
Step2: Find (f(-5)) and (f(3)) from the graph
From the graph, when (x=-5), (f(-5)=12). When (x = 3), (f(3)=10).
Step3: Substitute into the formula
Substitute (a=-5), (b = 3), (f(-5)=12), and (f(3)=10) into (\frac{f(b)-f(a)}{b - a}). We get (\frac{10 - 12}{3-(-5)}=\frac{-2}{8}=-\frac{1}{4}).
Answer:
(-\frac{1}{4})