Question

I need to verify this function is symmetric with respect to the y-axis. How would I go about doing that? Function: x^4-5x^2+3

Answer 1

`f(x) = x^4-5x^2+3` is symmetric to the y-axis

Explanation:

Given

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

Required

Determine if it is symmetric

First, we check if the function is even by calculating f(-x)

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

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

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

We have:

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

This implies that the function is even, and even functions are symmetric to the y-axis.

Hence:

`f(x) = x^4-5x^2+3` is symmetric to the y-axis