Difference Quotient
Examples, solutions, videos, worksheets, and activities to help PreCalculus students learn how to find the difference quotient of a function.
Related Pages
More Lessons for PreCalculus
Math Worksheets
The following figures show the Difference Quotient formula and graph. Scroll down the page for examples and step by step solutions.
Computing Difference Quotients
To find the slope of the secant line between two points in a function, we use difference quotients. Difference quotients are used with limits in the definition of the derivative and are important to understand, but can be difficult to compute and simplify. We can simplify difference quotients into a formula for finding the slope of a secant line.
The Difference Quotient
This video gives the formula for the difference quotient (the subtraction fraction) and do a couple examples of finding it for different functions.
Examples:
a) Let f(x) = 2x - 5; find f(x+h) - f(x)
b) Let f(x) = 3x + 2; find the difference quotient:
(f(x+h) - f(x))/h
The Difference Quotient
This video gives the formula for the difference quotient and do another example of finding it for a quadratic function.
Example:
Let f(x) = 2x2 - x + 5;
find and simplify the difference quotient
(f(x+h) - f(x))/h
Difference Quotient
Example:
Evaluate the difference quotient for f(x) = 4x2
Check out our most popular games!
Fraction Concoction Game:
Master fractions in the lab: mix, add, and subtract beakers to create the perfect concoction!
Fact Family Game:
Complete fact families and master the link between addition & subtraction and multiplication & division.
Number Bond Garden:
Clear the board by matching number pairs that sum to ten in this garden-themed mental math puzzle.
Online Addition Subtraction Game:
Practice your addition and subtraction skills to help the penguin find its mummy.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.