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 $-9 \\leq x \\leq 1$?

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-9 \\leq x \\leq 1$?

Answer

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function ( f(x) ) on the interval ([a, b]) is given by (\frac{f(b) - f(a)}{b - a}). Here, ( a=-9 ) and ( b = 1 ).

Step2: Find ( f(-9) ) and ( f(1) ) from the graph

From the graph, when ( x=-9 ), we can see that ( f(-9)=-8 ) (by looking at the point on the graph corresponding to ( x = - 9 )). When ( x = 1 ), ( f(1)=-2 ) (from the graph's point at ( x = 1 )).

Step3: Substitute into the formula

Substitute ( a=-9 ), ( b = 1 ), ( f(a)=-8 ), and ( f(b)=-2 ) into the formula: [ \frac{f(1)-f(-9)}{1-(-9)}=\frac{-2-(-8)}{1 + 9}=\frac{-2 + 8}{10}=\frac{6}{10}=\frac{3}{5}=0.6 ]

Answer:

(\frac{3}{5}) (or (0.6))