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)=2x^{6}+x^{8}\\)\\(\dots\\)determine whether the function is even, odd, or neither. choose the correct answer below.\\(\bigcirc\\) odd\\(\bigcirc\\) neither\\(\bigcirc\\) even

Explanation:

Step1: Define $h(-x)$

$$h(-x)=2(-x)^6 + (-x)^8$$

Step2: Simplify exponents

$$h(-x)=2x^6 + x^8$$

Step3: Compare to $h(x)$

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

Step4: Relate to symmetry

Even functions are symmetric about the y-axis.

Answer:

even
The function's graph is symmetric with respect to the y-axis.