1. The problem asks to determine the nature of the function $f$ based on its graph. 2. Recall the definitions: - A function $f$ is **one-to-one** if each $y$ value corresponds to exactly one $x$ value. - A function $f$ is **even** if $f(-x) = f(x)$ for all $x$ in the domain. - A function $f$ is **odd** if $f(-x) = -f(x)$ for all $x$ in the domain. - If none of these conditions hold, the function is **neither odd nor even**. 3. From the graph description: - The function passes through $(0,2)$ and $(-2,-1)$. - Check evenness: $f(2)$ is not given, but $f(-2) = -1$. - If $f$ were even, $f(2)$ should equal $f(-2) = -1$. - Check oddness: $f(-2) = -1$ and $-f(2)$ should equal $-1$; thus $f(2)$ should be $1$. 4. Since $f(2)$ is not given, but the function is decreasing from left to right and passes through $(0,2)$, it is unlikely that $f(2) = -1$ or $1$. 5. Also, the function is decreasing and passes through multiple $y$ values for different $x$, so it is likely one-to-one. 6. Conclusion: The function is **one-to-one**. Final answer: a) one-to-one.