# Finite Math Examples

Find the Average Rate of Change
,
Substitute using the average rate of change formula.
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.
Substitute the equation for and , replacing in the function with the corresponding value.
Simplify the expression.
Multiply the numerator and denominator of the complex fraction by .
Multiply by .
Combine.
Apply the distributive property.
Simplify by cancelling.
Cancel the common factor of .
Write as a fraction with denominator .
Factor out the greatest common factor .
Cancel the common factor.
Rewrite the expression.
Simplify.
Multiply and .
Divide by .
Simplify the numerator.
Remove parentheses around .
Raise to the power of .
Multiply by .
Raise to the power of .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine the numerators over the common denominator.
Simplify the numerator.
Cancel the common factor of .
Simplify.