3.1 Functions, 3.1 Relations and Functions

Difference Quotient: Linear Function

Example:  Find the difference quotient for f(x)=2x-9

The Difference Quotient:{f(x+h)-f(x)}/h

Solution:

The Difference Quotient Formula
{f(x+h)-f(x)}/h
Write the difference quotient for the given function
={2(x+h)-9-(2x-9)}/h
Use the distributive property
={2(x+h)-9-(2x-9)}/h
={2x+2h-9-2x+9}/h
Combine the like terms.  Only terms with h should remain in the numerator.
={2x+2h-9-2x+9}/h
={2h}/h
Cancel the common h from each term
={2h}/h
=2

The difference quotient for the function f(x)=2x-9 is {f(x+h)-f(x)}/h=2