# Precalculus Examples

,

Step 1

Step 1.1

The average rate of change of a function can be found by calculating the change in values of the two points divided by the change in values of the two points.

Step 1.2

Substitute the equation for and , replacing in the function with the corresponding value.

Step 2

Step 2.1

Simplify the numerator.

Step 2.1.1

Rewrite as .

Step 2.1.2

Pull terms out from under the radical, assuming positive real numbers.

Step 2.1.3

Any root of is .

Step 2.1.4

Multiply by .

Step 2.1.5

Subtract from .

Step 2.2

Simplify the denominator.

Step 2.2.1

Multiply by .

Step 2.2.2

Subtract from .