1. **State the problem:** We need to graph the piecewise function: $$f(x) = \begin{cases} 3 & \text{for } x < 1 \\ x + 2 & \text{for } x > 5 \end{cases}$$ 2. **Understand the function pieces:** - For $x < 1$, the function is constant at $y = 3$. This is a horizontal line extending left from $x=1$ but not including $x=1$. - For $x > 5$, the function is linear: $y = x + 2$. This line starts just to the right of $x=5$ (not including $x=5$) and extends to the right. 3. **Important points and open circles:** - At $x=1$, the value is not defined (open circle) on the horizontal line at $(1,3)$. - At $x=5$, the value is not defined (open circle) on the line $y = x + 2$, so at $(5,7)$. 4. **Graphing instructions:** - Draw a horizontal line at $y=3$ for all $x < 1$ with an open circle at $(1,3)$. - Draw the line $y = x + 2$ for all $x > 5$ with an open circle at $(5,7)$. Final answer: The graph consists of two disconnected pieces as described.