Question

1. find the average rate of change from x = -1 to x = 1.

Explanation:

Step1: Find f(-1) and f(1) from the graph

From the graph, when \( x = -1 \), the \( y \)-value ( \( f(-1) \)) is 6. When \( x = 1 \), the \( y \)-value ( \( f(1) \)) is 3.

Step2: Use the average rate of change formula

The formula for the average rate of change of a function \( f(x) \) from \( x = a \) to \( x = b \) is \( \frac{f(b) - f(a)}{b - a} \). Here, \( a = -1 \), \( b = 1 \), \( f(a)=f(-1) = 6 \), \( f(b)=f(1) = 3 \).

Substitute the values into the formula:
\( \frac{f(1) - f(-1)}{1 - (-1)}=\frac{3 - 6}{1 + 1}=\frac{-3}{2}=-1.5 \)

Answer:

\( -1.5 \) (or \( -\frac{3}{2} \))