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

Answer:

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

Step-by-step 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