use possible symmetry to determine whether the graph is the graph of an even function, an odd function, or a…

Explanation:

Step1: Recall function - symmetry rules

An even function has $f(x)=f( - x)$ and is symmetric about the y - axis. An odd function has $f(-x)=-f(x)$ and is symmetric about the origin.

Step2: Check points on the graph

We have the points $(-2,\frac{4}{9})$, $(0,\frac{4}{5})$, and $(2,\frac{4}{9})$. For $x = 2$ and $x=-2$, $f(2)=\frac{4}{9}$ and $f(-2)=\frac{4}{9}$. Since $f(2)=f(-2)$ for these points, and if the graph is symmetric about the y - axis for all points (by observing the general shape of the graph), the function satisfies the property of an even function. We can also note that for an odd - function, if $(x,y)$ is on the graph, then $(-x,-y)$ should be on the graph. Here, when $x = 2,y=\frac{4}{9}$ and when $x=-2,y=\frac{4}{9}$, not $y =-\frac{4}{9}$.

Answer:

The function is an even function.