Question

question 1, 2.2.10
decide whether the following statement is 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.
choose the correct answer below.
false
true

Explanation:

Step1: Consider a counter - example

A circle centered at the origin with equation $x^{2}+y^{2}=r^{2}$ is symmetric about the x - axis. If we replace $y$ with $-y$, the equation $x^{2}+(-y)^{2}=r^{2}$ (which simplifies to $x^{2}+y^{2}=r^{2}$) remains the same.

Step2: Check y - axis symmetry

For the circle $x^{2}+y^{2}=r^{2}$, if we replace $x$ with $-x$, the equation $(-x)^{2}+y^{2}=r^{2}$ (which simplifies to $x^{2}+y^{2}=r^{2}$) remains the same. So a graph can be symmetric about both x - axis and y - axis.

Answer:

False