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 $-6\\leq x\\leq - 1$?
Answer
Explanation:
Step1: Recall the formula for average rate of change
The formula for 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), (y=-10) (so (f(-6)=-10)), and when (x = - 1), (y=-10) (so (f(-1)=-10)).
Step3: Substitute into the formula
Substitute (a=-6), (b=-1), (f(a)=-10), and (f(b)=-10) into (\frac{f(b)-f(a)}{b - a}). We get (\frac{-10-(-10)}{-1-(-6)}=\frac{-10 + 10}{-1 + 6}).
Step4: Simplify the expression
(\frac{-10 + 10}{-1 + 6}=\frac{0}{5}=0).
Answer:
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