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Symmetry. Viviana C. Castellón East Los Angeles College MEnTe Mathematics Enrichment through Technology. A graph that is symmetric to the x-axis, can be seen as slicing a figure horizontally. In other words, for every point (x,y) on the graph, the point (x,-y) is also on the graph.

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symmetry

Symmetry

Viviana C. Castellón

East Los Angeles College

MEnTe

Mathematics Enrichment

through Technology

symmetric with respect to the x axis
A graph that is symmetric to the x-axis, can be seen as slicing a figure horizontally. In other words, for every point (x,y) on the graph, the point (x,-y) is also on the graph.Symmetric with Respect to the x-Axis
slide3
The figure illustrates symmetric with respect to the x-axis. The part of the graph above the x-axis is a reflection (mirror image) of the part below thex-axis.
testing for symmetry with respect to the x axis
Testing for Symmetrywith respect to the x-axis

Substitute -y for every y in the equation. If the equation is EXACTLY as the original equation, the graph is symmetric with respect to the x-axis.

testing for symmetry with respect to the x axis6
Testing for Symmetrywith respect to the x-axis

The following equation is given:

Substitute –y for every y.

Since the equation is EXACTLY the same as

the original equation, then the graph is

symmetric with respect to the x-axis.

the function could also be graphed to show that it is symmetric with respect to the x axis
The function could also be graphed to show that it is symmetric with respect to the x-axis.
slide9

After substituting a –y for every y, the equation is EXACTLY the same as the original. Therefore, the equation is symmetric with respect to the x-axis.

the function could also be graphed to show that it is symmetric with respect to the x axis10
The function could also be graphed to show that it is symmetric with respect to the x-axis.
slide12

After substituting a –y for every y, the equation is NOT EXACTLY the same as the original. Therefore, the equation is NOT symmetric with respect to the x-axis.

slide14

After substituting a –y for every y, the equation is NOT EXACTLY the same as the original. Therefore, the equation is NOT symmetric with respect to the x-axis.

the function could also be graphed to show that it is not symmetric with respect to the x axis
The function could also be graphed to show that it is NOT symmetric with respect to the x-axis.
slide17

After substituting a –y for every y, the equation is EXACTLY the same as the original. Therefore, the equation is symmetric with respect to the x-axis.

the function could also be graphed to show that it is symmetric with respect to the x axis18
The function could also be graphed to show that it is symmetric with respect to the x-axis.