Question

How do you determine if `f(x)=x^4+x^2+3` is an even or odd function?

Answer 1

even function

Explanation:

To determine if a function is odd/even ,consider the following.

• If f(x) = f( -x) , then f(x) is an even function

Even functions are symmetrical about the y-axis.

• If f( -x) = - f(x) , then f(x) is an odd function.

Odd functions have symmetry about the origin.

Test for even

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

Since f(x) = f( -x) , then function is even

Here is the graph of f(x). Note symmetry about y-axis.
graph{x^4+x^2+3 [-20, 20, -10, 10]}