1. Problem: Evaluate the absolute value function $|x|$ at $x=-3,0,3,100,-100$ and explain the piecewise definition and graph. 2. Recall the definition of absolute value. $$|x|=\begin{cases} x & \text{if } x>0 \\ 0 & \text{if } x=0 \\ -x & \text{if } x<0 \end{cases}$$ 3. Evaluate each given value. For $x=3$ since $3>0$ we use the first branch and get $|3|=3$. For $x=-3$ since $-3<0$ we use the third branch and get $|-3|=-(-3)=3$. For $x=0$ since $0=0$ we use the second branch and get $|0|=0$. For $x=100$ since $100>0$ we use the first branch and get $|100|=100$. For $x=-100$ since $-100<0$ we use the third branch and get $|-100|=-(-100)=100$. 4. Graph explanation. The graph of $y=|x|$ is a V-shaped curve with its vertex at $ (0,0) $ and symmetric about the $y$-axis. It has a global minimum at $y=0$ attained at $x=0$ and no maximum. Final answers: $|3|=3$, $|-3|=3$, $|0|=0$, $|100|=100$, $|-100|=100$.