Alabama Learning Exchange
Building Functions: Inverse Functions from Tables and Graphs
Is the inverse a function? Scholars learn how to examine a function to answer this question. Using an online interactive, they examine the properties of inverse functions to compare to the original function.
Shodor Education Foundation
Vertical Line Test
Connect the points to create a function. Using points given by the applet, pupils try to connect them to create a line that would pass the vertical line test. The resource keeps track of the number of sets the learner is able to identify...
CK-12 Foundation
Identify Functions and the Vertical Line Test: The Vertical Line Test
There's no easier test than the vertical line test. Learners drag a vertical line across the graphs of several relations in an interactive. They answer a set of challenge questions that focus on whether the graphs represent functions.
CK-12 Foundation
Algebraic Functions: Vertical Line Test
To be (a function) or not to be (a function). An easy-to-use interactive has pupils drag a vertical line onto several graphs to determine if they represent functions. Some challenge questions assess understanding of this idea.
CK-12 Foundation
Linear and Non-Linear Function Distinction: Domain and Range of a Function
Functions are special types of relations, but what makes them so special? Pupils use an interactive to slide a vertical line across six different graphs. Ten challenge questions then assess understanding of functions.
CK-12 Foundation
Vertical Line Test: Exploration
What do vertical lines have to do with functions? Individuals slide a vertical line through four different graphs. They use that vertical line test to determine if the graphs represent functions.
Willow Tree
Functions
What makes a function a function? Learn the criteria for a relation defined as a function both numerically and graphically. Once young mathematicians define a function, they use function notation to evaluate it.
Curated OER
Domain and Range
Relations, and functions, and line tests, oh my! An instructional slideshow demonstrates the definitions of a relation, a function, and the domain and range of a relation. Viewers then learn how to use mappings and vertical...
Curated OER
Functions and the Vertical Line Test
Students explore the concept of functions. In this function lesson, students determine if the graph is a function by using the vertical line test. Students use an applet to explore the vertical line test on a variety of graphs.
Mathematics Archives
Math Archives: Visual Calculus: Functions
Use this site to find the defintion of a function. The site offers a discussion on the vertical line test, symbolic, numerical and verbal discussions on the definition of a function.
Texas A&M University
Wtamu Virtual Math Lab: Intermediate Algebra
This site is a tutorial for students in algebra 2 or for those who need a refresher. The site has explanations, definitions, examples, practice problems and practice tests are found covering topics such as linear equations, graphing,...
Windstream
Ojk's Precalculus Study Page: Functions
An introduction to the basic terminology of functions, including how to use the vertical line test on the graph of a relation as a means of testing whether or not it is a function.
Shodor Education Foundation
Shodor Interactivate: Lesson: Functions and the Vertical Line Test
This lesson plan outlines an activity that allows students to explore the vertical line test for functions.
Texas Instruments
Texas Instruments: Relations and Functions
A function is a relation that assigns exactly one value of the dependent variable to each value of the independent variable. When a function is graphed, a vertical line can pass through the graph and touch only one point.
Texas A&M University
Wtamu Virtual Math Lab: Intermediate Algebra: Introduction to Functions
This introductory tutorial on functions offers important definitions, examples of functions, and practice exercises for you to complete and check.
Other
Mathn stuff.com: Vertical Line Test
Defines the vertical line test and provides a diagram showing graphs which pass and fail the test. Also provides several links for further information.
CK-12 Foundation
Ck 12: Algebra: Vertical Line Test
[Free Registration/Login may be required to access all resource tools.] Learn how to determine whether or not a relation is a function.
Purple Math
Purplemath: Functions Versus Relations
This lesson offers a thorough explanation of functions, domain and range, and how to find them. Includes multiple example problems and graphs. Great review tool for Algebra students.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Graph of Circle as a Function
Dr. Math, in a reply to a student question, describes how a circle can be a function.
Oswego City School District
Regents Exam Prep Center: Algebra 2: Definition of Inverse Function
An introductory look at the definition of an inverse function, the notation used for inverse functions, and tests used to determine whether a function will have an inverse. Several examples are provided for the student to scroll through...
University of North Carolina
University of North Carolina Wilmington: Graphs of Functions
Defining the graph of a function, vertical line test, characteristics of graphs, approximating relative extrema, and even and odd functions are covered with examples that include charts and graphs.
University of Vienna (Austria)
University of Vienna: Graph or Not Graph
Interactive quiz to determine whether each graph is representative of a function or not. Some graphs are discontinuous, some fail the vertical line test, and some actually are functions. After completion, the site gives a score to judge...
Cool Math
Coolmath: The Vertical Line Test
Explanation and examples for using the vertical line test.
CK-12 Foundation
Ck 12: Algebra: Vertical Line Test
[Free Registration/Login may be required to access all resource tools.] This concept introduces students to relations and what makes a relation a function.