Find the Symmetry y=|x|-5

There are three types of symmetry:

1. X-Axis Symmetry

2. Y-Axis Symmetry

3. Origin Symmetry

If ${\displaystyle (x,y)}$ exists on the graph, then the graph is symmetric about the:

1. X-Axis if ${\displaystyle (x,-y)}$ exists on the graph

2. Y-Axis if ${\displaystyle (-x,y)}$ exists on the graph

3. Origin if ${\displaystyle (-x,-y)}$ exists on the graph

Check if the graph is symmetric about the x-axis by plugging in ${\displaystyle -y}$ for ${\displaystyle y}$.

Since the equation is not identical to the original equation, it is not symmetric to the x-axis.

Not symmetric to the x-axis

Check if the graph is symmetric about the y-axis by plugging in ${\displaystyle -x}$ for ${\displaystyle x}$.

Since the equation is identical to the original equation, it is symmetric to the y-axis.

Symmetric with respect to the y-axis

Check if the graph is symmetric about the origin by plugging in ${\displaystyle -x}$ for ${\displaystyle x}$ and ${\displaystyle -y}$ for ${\displaystyle y}$.

Since the equation is not identical to the original equation, it is not symmetric to the origin.

Not symmetric to the origin

Determine the symmetry.

Symmetric with respect to the y-axis