
Concept explainers
To graph: The figure provided below such that it is symmetric with respect to x -axis.

Explanation of Solution
Given information:
The unsymmetrical graph is provided below,
Graph:
Reflect the provided graph about the x -axis such that the x -coordinate of each point remains the same and y -coordinate becomes negative.
The complete graph such that it is symmetric with respect to x -axis is provided below,
Interpretation:
Graph of the equation is symmetric with respect to x -axis means that graph is not changed when reflected about the x- axis.
The graph of an equation is symmetric about the x -axis, when y is replaced by
To graph: The figure provided below such that it is symmetric with respect to y -axis.

Explanation of Solution
Given information:
The unsymmetrical graph is provided below,
Graph:
Reflect the provided graph about the y -axis such that the x -coordinate of each point becomes negative and y -coordinate remains the same.
The complete graph such that it is symmetric with respect to y -axis is provided below,
Interpretation:
Graph of the equation is symmetric with respect to y -axis means that graph is not changed when reflected about the y- axis.
The graph of an equation is symmetric about the y -axis, when x is replaced by
To graph: The figure provided below such that it is symmetric with respect to origin.

Explanation of Solution
Given information:
The unsymmetrical graph is provided below,
Graph:
Reflect the provided graph about the origin such that the x -coordinate of each point becomes negative and y -coordinate also becomes negative.
The complete graph such that it is symmetric with respect to origin is provided below,
Interpretation:
Graph of the equation is symmetric with respect to origin means that graph is not changed when rotated
The equation is symmetric with respect to origin, when y is replaced by
Chapter 1 Solutions
Precalculus - A Custom Text for UNLV
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