Question

question: 3
the table below defines a quadratic function.

x	f(x)
-2	7
-1	2
0	-1
1	-2
2	-1

what is the average rate of change between x = -1 and x = 1?
a. undefined
b. -2
c. 0
d. -1

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \( f(x) \) between \( x = a \) and \( x = b \) is given by \( \frac{f(b) - f(a)}{b - a} \).

Step2: Identify \( a \), \( b \), \( f(a) \), and \( f(b) \)

Here, \( a = -1 \), \( b = 1 \). From the table, \( f(-1) = 2 \) and \( f(1) = -2 \).

Step3: Substitute into the formula

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

Step4: Simplify the expression

First, calculate the numerator: \( -2 - 2 = -4 \). Then, calculate the denominator: \( 1 + 1 = 2 \). Now, divide: \( \frac{-4}{2} = -2 \).

Answer:

B. -2