1. The problem asks to identify which relation is a function. 2. Recall that a function assigns exactly one output $y$ for each input $x$. 3. Analyze each option: - (a) $x = \sqrt{q} + 1$: Here $x$ depends on $q$, but $q$ is not defined as the input variable; this is ambiguous. - (b) $y = x^2 - 1$: This is a standard function where each $x$ has exactly one $y$. - (c) $x^2 + xy + y^2 = 3$: This is an implicit relation; it may assign multiple $y$ values for one $x$. - (d) $\{(1,2),(2,1),(1,3),(-1,4)\}$: The input $1$ maps to both $2$ and $3$, so not a function. 4. Therefore, only (b) is a function. Final answer: (b) $y = x^2 - 1$