Question

fill in each blank so that the resulting statement is true.
if $(x_1,f(x_1))$ and $(x_2,f(x_2))$ are distinct points on the graph of a function $f$, the average rate of change of $f$ from $x_1$ to $x_2$ is
select the correct answer below.
a. $\frac{f(x_2)+f(x_1)}{x_2 - x_1}$
b. $\frac{f(x_2)+f(x_1)}{x_2 + x_1}$
c. $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$
d. $\frac{f(x_2)-f(x_1)}{x_2 + x_1}$

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \(y = f(x)\) from \(x_1\) to \(x_2\) is given by the formula \(\frac{\text{Change in }y}{\text{Change in }x}\).
The change in \(y\) is \(f(x_2)-f(x_1)\) and the change in \(x\) is \(x_2 - x_1\).

Answer:

C. \(\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}\)