Question

Determine whether the function is even, odd, or neither. Then determine with respect to the y-axis, the origin, or neither.

Answer 1

Answer:

f(x) is even

f(x) is symmetrical about the y-axis

Explanation:

The given function is:

$f(x)=4x^4+x^{10}+3$

A function is even if f(x) = f(-x)

$\begin{gathered} f(-x)=4(-x)^4+(-x)^{10}+3 \\ \\ f(-x)=4x^4+x^{10}+3 \end{gathered}$

Since f(-x) = f(x), the function f(x) is an even function

Also, since f(x) = f(-x), the function f(x) is symmetrical about the y-axis