Respuesta :

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:

The given function is neither even nor odd.

Step-by-step explanation:

A function is an even function if

[tex]f(-x)=f(x)[/tex]

A function is an odd function if

[tex]f(-x)=-f(x)[/tex]

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,

[tex]f(3)=1[/tex]

[tex]f(-3)=2[/tex]

[tex]f(-3)\neq f(3)[/tex] and [tex]f(-3)\neq -f(3)[/tex]

Since [tex]f(-x)\neq f(x)[/tex] and [tex]f(-x)\neq -f(x)[/tex], therefore the given function is neither even nor odd.

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