Question

question
the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-3 \leq x \leq 1$?
answer attempt 1 out of 2
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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, \( a = -3 \) and \( b = 1 \).

Step2: Find \( f(-3) \) and \( f(1) \) from the graph

• For \( x = -3 \): Looking at the graph, when \( x = -3 \), the \( y \)-value ( \( f(-3) \)) is 10 (since the point at \( x = -3 \) has a \( y \)-coordinate of 10).
• For \( x = 1 \): Looking at the graph, when \( x = 1 \), the \( y \)-value ( \( f(1) \)) is 0 (since the point at \( x = 1 \) is on the \( x \)-axis, so \( y = 0 \)).

Step3: Calculate the average rate of change

Substitute \( a = -3 \), \( b = 1 \), \( f(-3) = 10 \), and \( f(1) = 0 \) into the formula:

$$ \frac{f(1) - f(-3)}{1 - (-3)}=\frac{0 - 10}{1 + 3}=\frac{-10}{4}=-\frac{5}{2}=-2.5 $$

Answer:

\( -2.5 \) (or \( -\frac{5}{2} \))