Question

determine whether the function is even, odd, or neither. then determine whether the functions graph is symmetric with respect to the y - axis, the origin, or neither.\\(h(x) = 3x^2 + x^{10}\\)\\(\dots\\)\
determine whether the function is even, odd, or neither. choose the correct answer below.\
\\(\bigcirc\\) even\
\\(\bigcirc\\) neither\
\\(\bigcirc\\) odd\
determine whether the graph of the function is symmetric with respect to the y - axis, the origin, or neither. select all that apply.\
\\(\square\\) y - axis\
\\(\square\\) origin\
\\(\square\\) neither

Explanation:

Step1: Define even function test

A function is even if $h(-x) = h(x)$.

Step2: Compute $h(-x)$

$$\begin{align*} h(-x)&=3(-x)^2 + (-x)^{10}\\ &=3x^2 + x^{10} \end{align*}$$

Step3: Compare $h(-x)$ and $h(x)$

Since $h(-x)=h(x)$, the function is even.

Step4: Link even function to symmetry

Even functions are symmetric about the y-axis.

Answer:

Determine whether the function is even, odd, or neither:
even

Determine whether the graph of the function is symmetric with respect to the y-axis, the origin, or neither:
y-axis