1. **State the problem:** Graph each equation and determine if it is a function. 2. **Equation a: $y = -2$** - This is a horizontal line where $y$ is always $-2$ regardless of $x$. - Table of values: $$\begin{array}{c|c} x & y \\\hline -3 & -2 \\ 0 & -2 \\ 4 & -2 \end{array}$$ - Graph these points and draw a horizontal line through $y = -2$. - Since for each $x$ there is exactly one $y$, it passes the vertical line test. - **Conclusion:** $y = -2$ is a function. 3. **Equation b: $x = 3$** - This is a vertical line where $x$ is always $3$ regardless of $y$. - Table of values: $$\begin{array}{c|c} x & y \\\hline 3 & -2 \\ 3 & 0 \\ 3 & 4 \end{array}$$ - Graph these points and draw a vertical line through $x = 3$. - This line fails the vertical line test because for $x=3$ there are multiple $y$ values. - **Conclusion:** $x = 3$ is not a function. 4. **Summary:** - A function assigns exactly one output $y$ for each input $x$. - Horizontal lines like $y = -2$ are functions. - Vertical lines like $x = 3$ are not functions. **Final answers:** - $y = -2$ is a function. - $x = 3$ is not a function.