the function ( y = f(x) ) is graphed below. what is the average rate of change of the function ( f(x) ) on…
the function ( y = f(x) ) is graphed below. what is the average rate of change of the function ( f(x) ) on the interval ( -4 leq x leq -3 )?
Answer
Explanation:
Step1: Recall the formula for average rate of change
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=-4) and (b = - 3).
Step2: Find (f(-4)) and (f(-3)) from the graph
From the graph, when (x=-4), (y=-80) (so (f(-4)=-80)), and when (x = - 3), (y = 60) (so (f(-3)=60)).
Step3: Substitute into the formula
Substitute (a=-4), (b=-3), (f(a)=-80), and (f(b)=60) into (\frac{f(b)-f(a)}{b - a}). We get (\frac{60-(-80)}{-3-(-4)}=\frac{60 + 80}{-3 + 4}).
Step4: Simplify the expression
(\frac{60+80}{-3 + 4}=\frac{140}{1}=140).
Answer:
(140)