Question

is f even, odd, or neither?
○ even
● odd
○ neither
explain your reasoning.
● it is symmetric about the origin.
○ it is symmetric with respect to the y - axis.
○ it is symmetric with respect to the x - axis.
○ it is not symmetric about the origin or the y - axis.
is g even, odd, or neither?
● even
○ odd
○ neither
explain your reasoning.
○ it is symmetric about the origin.
○ it is symmetric with respect to the y - axis.
○ it is symmetric with respect to the x - axis.
○ it is not symmetric about the origin or the y - axis.

Explanation:

For function $f$:

• An odd function is symmetric about the origin, meaning for every point $(x,y)$ on the graph, $(-x,-y)$ is also on the graph. The given graph matches this symmetry.

For function $g$:

• An even function is symmetric about the y-axis, meaning for every point $(x,y)$ on the graph, $(-x,y)$ is also on the graph. This defines the symmetry for an even function.

Answer:

Is $f$ even, odd, or neither?
odd
Explain your reasoning.
It is symmetric about the origin.

Is $g$ even, odd, or neither?
even
Explain your reasoning.
It is symmetric with respect to the y-axis.