A function is even if the graphic is symmetric with respect to the y-axis.
You can symbolize an even function as -f(x)=f(x) for all values of x on the domain of the function f.
A)
[tex]|y|=x^2[/tex]The expression |y| indicates that its the absolute value of y. This means that y can be positive or negative.
[tex]\begin{gathered} -y=x^2 \\ and \\ y=x^2 \end{gathered}[/tex]This function is even.
B)
[tex]y=-2|x|[/tex]In this example x is expressed as an absolute value and can be either positive or negative:
This function is symetrical with respect to the y-axis, so it an even function.
C)
[tex]y^2=|x|+1[/tex][tex]\begin{gathered} y^2=-x+1 \\ \text{and} \\ y^2=x+1 \end{gathered}[/tex]This function is not symetrical with respect to the y-axis
D)
[tex]y=|x+6|[/tex]This function is not symmetrial with respect to the y-axis
