1. The problem asks to classify each of the five expressions as functions or not functions. 2. Recall that a function assigns exactly one output for each input. 3. Expression 1: $y = |x| + xy$ - For each $x$, $y$ is defined uniquely by this expression, so it is a function. 4. Expression 2: $y = \lfloor x \rfloor + xy$ - $\lfloor x \rfloor$ is the greatest integer function, which is a function. - The expression defines $y$ uniquely for each $x$, so it is a function. 5. Expression 3: $y^{2/3} = x$ - To check if $y$ is a function of $x$, solve for $y$: $$y = \pm x^{3/2}$$ - There are two possible $y$ values for each positive $x$, so it is not a function. 6. Expression 4: $x^4 + y^4 = 4$ - For a given $x$, there can be multiple $y$ values satisfying the equation. - Hence, $y$ is not a function of $x$. 7. Expression 5: $y = x^{2/3}$ - For each $x$, $y$ is uniquely defined. - So, it is a function. Final classification: yes; yes; no; no; yes