1. **State the problem:** We are given a piecewise function: $$f(x) = \begin{cases} 4x + 17 & \text{for } x < -4 \\ -4 & \text{for } x \geq 0 \end{cases}$$ We need to understand or solve for values of $f(x)$ based on $x$. 2. **Analyze each piece:** - For $x < -4$, the function is linear: $f(x) = 4x + 17$. - For $x \geq 0$, the function is constant: $f(x) = -4$. 3. **Evaluate at boundary points:** - At $x = -4$, the function is not defined by the first piece since it is strictly less than $-4$. - At $x = 0$, $f(0) = -4$ by the second piece. 4. **Find the value of $f(x)$ at some points:** - For $x = -5$ (which is less than $-4$): $$f(-5) = 4(-5) + 17 = -20 + 17 = -3$$ - For $x = 1$ (which is greater than or equal to $0$): $$f(1) = -4$$ 5. **Summary:** - For any $x < -4$, use $f(x) = 4x + 17$. - For any $x \geq 0$, $f(x) = -4$. - The function is not defined for $-4 \leq x < 0$ based on the given definition. **Final answer:** The piecewise function is as given, and values can be computed accordingly.