Algebra 1
Q.21 Checkpoint: Average rate of change 179
Which of the following functions have an average rate of change equal to 0 on the interval from \( x=-2 \) to \( x=2 \) ? Select all that apply.
\[
f(x)=7-3 x
\]
\[
f(x)=7-3 x^{2}
\]
\[
f(x)=7 x
\]
\[
f(x)=7
\]
Answer
\(f_4(-2) = 7 \), \(f_4(2) = 7 \), Average rate of change: \(\frac{f_4(2) - f_4(-2)}{2 - (-2)} = \frac{7 - 7}{4} = 0 \)
Step 1 ：\(f_1(-2) = 7 - 3(-2) = 13 \), \(f_1(2) = 7 - 3(2) = 1 \), Average rate of change: \(\frac{f_1(2) - f_1(-2)}{2 - (-2)} = \frac{1 - 13}{4} = -3 \)
Step 2 ：\(f_2(-2) = 7 - 3(-2)^2 = 7 - 12 = -5 \), \(f_2(2) = 7 - 3(2)^2 = 7 - 12 = -5 \), Average rate of change: \(\frac{f_2(2) - f_2(-2)}{2 - (-2)} = \frac{-5 - (-5)}{4} = 0 \)
Step 3 ：\(f_3(-2) = 7(-2) = -14 \), \(f_3(2) = 7(2) = 14 \), Average rate of change: \(\frac{f_3(2) - f_3(-2)}{2 - (-2)} = \frac{14 - (-14)}{4} = 7 \)
Step 4 ：\(f_4(-2) = 7 \), \(f_4(2) = 7 \), Average rate of change: \(\frac{f_4(2) - f_4(-2)}{2 - (-2)} = \frac{7 - 7}{4} = 0 \)
