42. for f(x)=x² - 4x + 4, what is the average rate of change over 1,3? a. -1 b. 1 c. 0 d. 2

Answer:

C. 0

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 1$, $b = 3$, and $f(x)=x^{2}-4x + 4$.

Step2: Calculate $f(1)$

Substitute $x = 1$ into $f(x)$: $f(1)=1^{2}-4\times1 + 4=1 - 4 + 4=1$.

Step3: Calculate $f(3)$

Substitute $x = 3$ into $f(x)$: $f(3)=3^{2}-4\times3 + 4=9-12 + 4=1$.

Step4: Calculate the average rate of change

$\frac{f(3)-f(1)}{3 - 1}=\frac{1 - 1}{2}=\frac{0}{2}=0$.