This leskid will teach you exactly how to test for symmetry. You have the right to test the graph of a relation for symmetry with respect to the x-axis, y-axis, and the origin. In this leschild, we will certainly confirm symmeattempt algebraically.

You are watching: Symmetric with respect to the x axis

Test for symmetry through respect to the x-axis.

The graph of a relation is symmetric through respect to the x-axis if for eextremely suggest (x,y) on the graph, the point (x, -y) is additionally on the graph. To examine for symmetry with respect to the x-axis, simply relocation y via -y and also view if you still get the very same equation. If you carry out get the same equation, then the graph is symmetric via respect to the x-axis.


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

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


Test for symmeattempt with respect to the y-axis.

The graph of a relation is symmetric through respect to the y-axis if for eexceptionally suggest (x,y) on the graph, the allude (-x, y) is also on the graph.To inspect for symmeattempt via respect to the y-axis, simply rearea x through -x and see if you still acquire the very same equation. If you perform acquire the same equation, then the graph is symmetric with respect to the y-axis.


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

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

Test for symmetry via respect to the origin.

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The graph of a relation is symmetric via respect to the beginning if for eexceptionally suggest (x,y) on the graph, the point (-x, -y) is also on the graph.To examine for symmetry through respect to the origin, simply replace x via -x and y through -y and check out if you still acquire the very same equation. If you execute acquire the very same equation, then the graph is symmetric through respect to the origin.


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Example #3:is 2xy = 12 symmetric via respect to the origin?Relocation x with -x  and y through -y in the equation.2(-x × -y) = 122xy = 12Because replacing x with -x and also y via -y provides the same equation, the equation  2xy = 12  is symmetric via respect to the origin.


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Everything you should prepare for a vital exam! K-12 tests, GED math test, standard math tests, geometry tests, algebra tests. 


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