1. **State the problem:** Write a piecewise function for the absolute value of $x+3$. 2. **Recall the definition of absolute value:** For any expression $A$, the absolute value $|A|$ is defined as: $$|A| = \begin{cases} A & \text{if } A \geq 0 \\ -A & \text{if } A < 0 \end{cases}$$ 3. **Apply this to $x+3$:** - When $x+3 \geq 0$, which means $x \geq -3$, the function is $x+3$. - When $x+3 < 0$, which means $x < -3$, the function is $-(x+3)$. 4. **Write the piecewise function:** $$f(x) = |x+3| = \begin{cases} x+3 & \text{if } x \geq -3 \\ -(x+3) & \text{if } x < -3 \end{cases}$$ 5. **Explain in simple terms:** The absolute value makes any negative input positive by flipping its sign. So for values of $x$ less than $-3$, we take the negative of $x+3$ to make it positive. For values greater or equal to $-3$, $x+3$ is already positive or zero, so we keep it as is.