Question

question 4
what is the average rate of change for the given graph over the interval $-2 \leq x \leq 4$

Explanation:

Step1: Find f(-2) and f(4)

From the graph, at \( x = -2 \), the \( y \)-value (f(-2)) is -3. At \( x = 4 \), the \( y \)-value (f(4)) is 6.

Step2: Use average rate of change formula

The formula for average rate of change over \([a, b]\) is \(\frac{f(b) - f(a)}{b - a}\). Here, \( a = -2 \), \( b = 4 \), \( f(a) = -3 \), \( f(b) = 6 \).
Substitute values: \(\frac{6 - (-3)}{4 - (-2)} = \frac{6 + 3}{4 + 2} = \frac{9}{6} = \frac{3}{2}\)

Answer:

\(\frac{3}{2}\)