Find the Symmetry y=3-|x|

There are three types of symmetry:

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

Check if the graph is symmetric about the ${\displaystyle x}$-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.

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

Make ${\displaystyle -x}$ positive.

Since the equation is identical to the original equation, it is symmetric 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 ${\displaystyle y}$.

Make ${\displaystyle -x}$ positive.

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

Determine the symmetry.