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.\\(g(x)=x^{2}+4x\\)\\(\\)\\(\\)determine whether the function is even, odd, or neither. choose the correct answer below\\(\\)\\(\circ\\) even\\(\\)\\(\circ\\) odd\\(\\)\\(\circ\\) neither

Explanation:

Step1: Compute $g(-x)$

Substitute $-x$ into $g(x)$:
$g(-x) = (-x)^2 + 4(-x) = x^2 - 4x$

Step2: Compare to $g(x)$ and $-g(x)$

First, $-g(x) = -(x^2 + 4x) = -x^2 - 4x$.
Since $g(-x)
eq g(x)$ and $g(-x)
eq -g(x)$, the function is neither even nor odd.

Step3: Relate to symmetry

Even functions are symmetric about the y-axis, odd functions about the origin. Since this function is neither, its graph has neither symmetry.

Answer:

neither
The function's graph is symmetric with respect to neither the y-axis nor the origin.