Question

Is this function even, odd, or neither?

Answer 1

when a function is even, they have symmetry with respect to the y-axis, what does that mean? well, the graph to the right-side of the y-axis is just a mirror image of the graph to the left-side of the y-axis.

when a function is odd, the symmetry is with respect to the origin, meaning, the graph to the right-side of the y-axis, is a mirror image of the one on the left-bottom-upside-down. So, you take a photo of the right-side graph,flip it over the x-axis, and then flip it again over the y-axis.

now, this one shows neither of those behaviours.

Answer 2

The given function is neither even nor odd.

Explanation:

A function is an even function if

`f(-x)=f(x)`

A function is an odd function if

`f(-x)=-f(x)`

From the given graph it is clear that graph is passing though the points (-3,2), (-1,2), (0,1/2), (1/2,0), (1,-1), (2,-1) and (3,1).

Here,

`f(3)=1`

`f(-3)=2`

`f(-3)\\eq f(3)` and
`f(-3)\\eq -f(3)`

Since
`f(-x)\\eq f(x)` and
`f(-x)\\eq -f(x)`, therefore the given function is neither even nor odd.