Question

I need to verify this function is symmetric with respect to the y-axis. How would I go about doing that?

h(x)=x^4-5x^2+3

Answer 1

Yes, the function is symmetric about y-axis.

Explanation:

To check whether the function is symmetric with respect to y-axis, replace each x as -x and simplify.

If h(x) = h(-x) then it is symmetric about y-axis.

Let's find h(-x) now.

h(-x)=
`(-x)^4} -5(-x)^(2) +3`

Let's simplify it

h(-x)=
`x^(4)-5x^(2) +3`

Here, h(x) = h(-x). The function is symmetric about y-axis.