Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-4 \leq x \leq 0$?

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, \( a = -4 \) and \( b = 0 \).

Step2: Find \( f(-4) \) and \( f(0) \) from the graph

From the graph, when \( x = -4 \), the function value \( f(-4) = 0 \) (since the point is on the x - axis). When \( x = 0 \), the function value \( f(0)=- 8 \) (from the point on the y - axis).

Step3: Substitute into the formula

Substitute \( a=-4 \), \( b = 0 \), \( f(-4)=0 \) and \( f(0)=-8 \) into the formula \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{f(0)-f(-4)}{0-(-4)}=\frac{-8 - 0}{0 + 4}=\frac{-8}{4}=-2\).

Answer:

\(-2\)