This lesson will teach you how to test for symmetry. You can test the graph of a relation because that symmetry v respect come the x-axis, y-axis, and the origin. In this lesson, we will confirm the contrary algebraically.

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## Test for symmetry with respect come the x-axis.

The graph the a relationship is symmetric through respect to the x-axis if for every suggest (x,y) on the graph, the point (x, -y) is additionally on the graph. To examine for symmetry through respect to the x-axis, simply replace y v -y and see if girlfriend still acquire the same equation. If you do acquire the very same equation, then the graph is symmetric with respect to the x-axis.

Example #1:is x = 3y4 - 2 symmetric v respect to the x-axis?Replace y through -y in the equation.X = 3(-y)4 - 2X = 3y4 - 2

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

## Test for symmetry with respect come the y-axis.

The graph the a relation is symmetric v respect come the y-axis if for every allude (x,y) ~ above the graph, the allude (-x, y) is additionally on the graph.To inspect for symmetry through respect to the y-axis, simply replace x v -x and see if girlfriend still obtain the very same equation. If you do get the very same equation, then the graph is symmetric with respect to the y-axis.

Example #2:is y = 5x2 + 4 symmetric through respect to the x-axis?Replace x with -x in the equation.Y = 5(-x)2 + 4Y = 5x2 + 4

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

## Test for symmetry v respect come the origin.See more: I Just Want To Live My Life, I Want To Live My Life All Alone

The graph the a relationship is symmetric v respect to the beginning if because that every point (x,y) on the graph, the suggest (-x, -y) is also on the graph.To check for symmetry through respect come the origin, just replace x v -x and also y through -y and also see if girlfriend still acquire the same equation. If girlfriend do obtain the very same equation, then the graph is symmetric v respect come the origin.

Example #3:is 2xy = 12 symmetric through respect to the origin?Replace x v -x  and y with -y in the equation.2(-x × -y) = 122xy = 12Since instead of x with -x and also y through -y provides the exact same equation, the equation  2xy = 12  is symmetric with respect to the origin.

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