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.
$f(x)=x^{5}+6x$
determine whether the function is even, odd, or neither. choose the correct answer below.

• even
• odd
• neither

determine whether the graph of the function is symmetric with respect to the y - axis, the origin, or neither. select all that apply.

• neither
• y - axis
• origin

Explanation:

Step1: Define $f(-x)$

$f(-x) = (-x)^5 + 6(-x)$

Step2: Simplify $f(-x)$

$f(-x) = -x^5 - 6x = -(x^5 + 6x)$

Step3: Compare to $-f(x)$

$-f(x) = -(x^5 + 6x)$
Since $f(-x) = -f(x)$, the function is odd.

Step4: Relate to symmetry

Odd functions are symmetric about the origin.

Answer:

1. odd
2. origin