Question

fill in each blank so that the resulting statement is true. if (x₁, f(x₁)) and (x₂, f(x₂)) are distinct points on the graph of a function f, the average rate of change of f from x₁ to x₂ is ______. select the correct answer below. a. $\frac{f(x₂)+f(x₁)}{x₂ - x₁}$ b. $\frac{f(x₂)-f(x₁)}{x₂ + x₁}$ c. $\frac{f(x₂)-f(x₁)}{x₂ - x₁}$ d. $\frac{f(x₂)+f(x₁)}{x₂ + x₁}$

Explanation:

Step1: Recall average rate - of - change formula

The average rate of change of a function \(y = f(x)\) from \(x = x_1\) to \(x=x_2\) is given by the ratio of the change in the function values to the change in the \(x\) - values.
The change in the function values is \(f(x_2)-f(x_1)\) and the change in the \(x\) - values is \(x_2 - x_1\).

Step2: Write the formula

The average rate of change is \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}\).

Answer:

C. \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}\)