1. **State the problem:** Identify which of the given relations is not a function. 2. **Recall the definition of a function:** A function assigns exactly one output $y$ for each input $x$. 3. **Test each relation:** - $y = \sqrt{x}$: For each $x \geq 0$, there is exactly one non-negative $y$, so this is a function. - $y^2 = x - 5$: Solving for $y$ gives $y = \pm\sqrt{x-5}$ which means for some $x$, there are two possible $y$ values; this violates the function definition. - $y = 3x - 4$: This is a linear equation; each $x$ corresponds to exactly one $y$, so this is a function. - $y = \frac{1}{x}$: For every $x \neq 0$, there is exactly one $y$, so this is a function. 4. **Conclusion:** The relation $y^2 = x - 5$ is not a function because one $x$ maps to two values of $y$. **Final answer:** $y^2 = x - 5$ is not a function.