1. **Problem:** Determine whether the function $f(x)$ is one-to-one (injective). 2. **Definition:** A function is one-to-one if each $y$-value corresponds to exactly one $x$-value. In other words, if $f(a) = f(b)$ implies $a = b$. 3. **Reasoning:** From the description, the graph passes through the origin, rises to the right, and falls to the left, resembling a parabola or absolute value function. 4. **Analysis:** Both parabolas and absolute value functions are not one-to-one because they fail the horizontal line test: a horizontal line intersects the graph at more than one point. 5. **Conclusion:** Therefore, $f(x)$ is **not one-to-one** because there exist distinct $x$ values with the same $f(x)$ value. 1. **Problem:** Determine whether the function $f(x)$ is onto (surjective). 2. **Definition:** A function is onto if every possible $y$-value in the codomain has a corresponding $x$-value in the domain. 3. **Reasoning:** The graph rises to the right and falls to the left, but since it is shaped like a parabola or absolute value, the range is $[0, \, \infty)$ or similar. 4. **Analysis:** If the codomain is all real numbers, the function is not onto because negative $y$-values are not achieved. 5. **Conclusion:** Therefore, $f(x)$ is **not onto** if the codomain is all real numbers, because it does not cover all $y$-values. **Final answers:** - $f(x)$ is not one-to-one. - $f(x)$ is not onto (assuming codomain is all real numbers).