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.

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.

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.See more: The U.S. Public Health Service (Phs) Requires Institutions To:

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.

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.

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

Recommfinished Scientific Notation Quiz Graphing Slope Quiz Adding and also Subtracting Matrices Quiz   Factoring Trinomials Quiz  Solving Absolute Value Equations Quiz   Order of Operations Quiz Types of angles quiz

About me :: Privacy plan :: Disclaimer :: Awards :: Donate Facebook web page :: Pinteremainder pins