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 $-7 \\leq x \\leq -5$?

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-7 \\leq x \\leq -5$?

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 = -7 ) and ( b = -5 ).

Step2: Find ( f(-7) ) and ( f(-5) ) from the graph

From the graph, when ( x = -7 ), the corresponding ( y )-value (i.e., ( f(-7) )) is ( 0 ) (since the point is on the x - axis at ( x=-7 )). When ( x = -5 ), the corresponding ( y )-value (i.e., ( f(-5) )) is ( 4 ) (by looking at the graph, the point at ( x = -5 ) has a ( y )-coordinate of ( 4 )).

Step3: Substitute into the formula

Substitute ( a=-7 ), ( b = -5 ), ( f(-7)=0 ) and ( f(-5) = 4 ) into the formula (\frac{f(b)-f(a)}{b - a}). We get (\frac{f(-5)-f(-7)}{-5-(-7)}=\frac{4 - 0}{-5 + 7}=\frac{4}{2}=2).

Answer:

( 2 )