Test for symmetry


You can test the graph of a relation for symmetry with respect to the x-axis, y-axis, and the origin.

Test for symmetry with respect to the x-axis.

The graph of a relation is symmetric with respect to the x-axis if for every point (x,y) on the graph, the point (x, -y) is also on the graph.


Example #1:


is x = 3y4 - 2 symmetric with respect to the x-axis?

Replace y with -y in the equation.

X = 3(-y)4 - 2

X = 3y4 - 2

Since replacing y with -y gives the same equation, the equation x = 3y4 - 2 is symmetric with respect to the x-axis.


Test for symmetry with respect to the y-axis.


The graph of a relation is symmetric with respect to the y-axis if for every point (x,y) on the graph, the point (-x, y) is also on the graph.

Symmetry with respect to y-axis


Example #2:


is y = 5x2 + 4 symmetric with respect to the x-axis?

Replace x with -x in the equation.

Y = 5(-x)2 + 4

Y = 5x2 + 4

Since replacing x with -x gives the same equation, the equation y = 5x2 + 4 is symmetric with respect to the y-axis.


Test for symmetry with respect to the origin.


The graph of a relation is symmetric with respect to the origin if for every point (x,y) on the graph, the point (-x, -y) is also on the graph.

Symmetry with respect to the origin

Example #3:

is 2xy = 12 symmetric with respect to the origin?

Replace x with -x  and y with -y in the equation.

2(-x × -y) = 12

2xy = 12

Since replacing x with -x and y with -y gives the same equation, the equation 
2xy = 12  is symmetric with respect to the origin.




Recent Articles

  1. Factoring using the Box Method

    Sep 18, 19 01:16 PM

    Factoring using the box method. Common pitfalls to avoid when using this method.

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

            Follow me on Pinterest

Math quizzes

 Recommended

Scientific Notation Quiz

Graphing Slope Quiz

Adding and Subtracting Matrices Quiz  

Factoring Trinomials Quiz 

Solving Absolute Value Equations Quiz  

Order of Operations Quiz

Types of angles quiz


Tough algebra word problems

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Recent Articles

  1. Factoring using the Box Method

    Sep 18, 19 01:16 PM

    Factoring using the box method. Common pitfalls to avoid when using this method.

    Read More

K-12 math tests


Everything you need to prepare for an important exam!

K-12 tests, GED math test, basic math tests, geometry tests, algebra tests. 

Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.