1. **State the problem:** We have a piecewise function: $$f(x) = \begin{cases} 2x + 1 & \text{if } x \leq 2 \\ -4 & \text{if } x > 2 \end{cases}$$ We need to find $f(5)$, $f(2)$, and $f(-1)$. 2. **Evaluate $f(5)$:** Since $5 > 2$, use the second piece: $$f(5) = -4$$ 3. **Evaluate $f(2)$:** Since $2 \leq 2$, use the first piece: $$f(2) = 2(2) + 1 = 4 + 1 = 5$$ 4. **Evaluate $f(-1)$:** Since $-1 \leq 2$, use the first piece: $$f(-1) = 2(-1) + 1 = -2 + 1 = -1$$ 5. **Summary of values:** $$f(5) = -4, \quad f(2) = 5, \quad f(-1) = -1$$ 6. **Sketching the function:** - For $x \leq 2$, the graph is the line $y = 2x + 1$. - For $x > 2$, the graph is the constant line $y = -4$. - At $x=2$, the function value is $5$ (from the first piece). This creates a line segment ending at $(2,5)$ and a horizontal line starting just after $x=2$ at $y=-4$. Final answers: $$f(5) = -4, \quad f(2) = 5, \quad f(-1) = -1$$