Questions: Determine whether the function is even, odd, or neither. Then determine whether the function's graph is symmetric with respect to the y-axis, the origin, or neither. f(x)=x sqrt(6-x^8) Determine whether the function is even, odd, or neither. Choose the correct answer below. neither odd even

Determine whether the function is even, odd, or neither. Then determine whether the function's graph is symmetric with respect to the y-axis, the origin, or neither.
f(x)=x sqrt(6-x^8)

Determine whether the function is even, odd, or neither. Choose the correct answer below.
neither
odd
even

Transcript text: Determine whether the function is even, odd, or neither. Then determine whether the function's graph is symmetric with respect to the $y$-axis, the origin, or neither. \[ f(x)=x \sqrt{6-x^{8}} \] Determine whether the function is even, odd, or neither. Choose the correct answer below. neither odd even

Solution

Solution Steps

Step 1: Determine if the function is even, odd, or neither

To determine the parity of the function, we evaluate if $f(x) = f(-x)$ for evenness and if $f(-x) = -f(x)$ for oddness. After evaluation, we find that the function is odd.

Step 2: Determine the symmetry of the function's graph

Based on the parity, we can infer that the graph of the function is symmetric with respect to the origin.