Question

1. determine the average rate of change over the interval -2, 2. a) 1 b) 4 c) -4 d) -1

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \( f(x) \) over the interval \([a, b]\) is given by \(\frac{f(b) - f(a)}{b - a}\).

Step2: Identify the values of \( a \), \( b \), \( f(a) \), and \( f(b) \)

For the interval \([-2, 2]\), \( a = -2 \) and \( b = 2 \). From the graph, when \( x = -2 \), \( f(-2) = 4 \) (the point \((-2, 4)\)), and when \( x = 2 \), \( f(2) = 0 \) (the point \((2, 0)\)).

Step3: Substitute into the formula

Substitute \( a = -2 \), \( b = 2 \), \( f(-2) = 4 \), and \( f(2) = 0 \) into the formula:

$$ \frac{f(2) - f(-2)}{2 - (-2)} = \frac{0 - 4}{2 + 2} $$

Step4: Simplify the expression

First, simplify the numerator: \( 0 - 4 = -4 \). Then, simplify the denominator: \( 2 + 2 = 4 \). So, \(\frac{-4}{4} = -1\).

Answer:

d) -1