Q. 10 - Precalculus Enhanced with Graphing Utilities

Question

True or False : 

If a graph is symmetric with respect to the x-axis, then it cannot be symmetric with respect to the y-axis.

Step-by-Step Solution

Answer

The given statement is False .

Step 1: Given information:

The given statement is :

If a graph is symmetric with respect to the x-axis, then it cannot be symmetric with respect to the y-axis.

Step 2:

If a graph is symmetric with respect to the x-axis, then it need not be always true that it cannot be symmetric with respect to y-axis.

Example: Equation of circle with center as origin $\left(0,0\right)$  and radius is 1 unit,

$ie, x^2+y^2=1.$