7. if f(x)=2x - 1, what is the average rate of change over 4, 8? a. 1 b. 3 c. 2 d. 4

Answer:

C. 2

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, $a = 4$, $b = 8$ and $f(x)=2x - 1$.

Step2: Calculate $f(8)$

Substitute $x = 8$ into $f(x)$: $f(8)=2\times8 - 1=16 - 1=15$.

Step3: Calculate $f(4)$

Substitute $x = 4$ into $f(x)$: $f(4)=2\times4 - 1=8 - 1=7$.

Step4: Calculate the average rate of change

$\frac{f(8)-f(4)}{8 - 4}=\frac{15 - 7}{4}=\frac{8}{4}=2$.