Please help me I need this to be right or I could fail this class

Question

A student says that the function f(x)=3x^4+5x^2+1 is an even function. Is the student's statement true or not true, and why?

A. The student's claim is true, because for any input of x, f(x)=f(−x)

B. The student's claim is true, because for any input of x, f(x)=−f(x).

C. The student's claim is not true, because for any input of x, f(x)=−f(x).

D. The student's claim is not true, because for any input of x, f(x)=f(−x).

Answer 1

A. The student's claim is true, because for any input of x, f(x)=f(−x)

When you input -x into the equation, the equation simplifies back to the original equation,

proving that f(x)=f(-x), which indicates that the equation is an even function.

Answer 2

This function notation, f(x)=f(-x), means that when a number x or its opposite -x are used as input, the output remains unchanged.

The graph of an even function is symmetric with respect to the y-axis. Take a look at the graph of your polynomial f(x)=3x^4+5x^2+1 in the online graphing calculator Desmos.com

Is it symmetric with respect to the y-axis? ;)