Question

the function ( y = f(x) ) is graphed below. what is the average rate of change of the function ( f(x) ) on the interval ( -8 leq x leq -7 )?

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, \( a = -8 \) and \( b = -7 \).

Step2: Find \( f(-8) \) and \( f(-7) \) from the graph

From the graph, when \( x = -8 \), the point is on the x - axis, so \( f(-8)=0 \). When \( x=-7 \), we can see from the graph (by looking at the coordinates of the point) that \( f(-7) = 2 \) (assuming the grid has appropriate scaling, and the point at \( x = -7 \) has a y - value of 2).

Step3: Calculate the average rate of change

Substitute \( a=-8 \), \( b = -7 \), \( f(-8)=0 \) and \( f(-7)=2 \) into the formula:
\[
\frac{f(-7)-f(-8)}{-7-(-8)}=\frac{2 - 0}{-7 + 8}=\frac{2}{1}=2
\]

Answer:

2