1. The problem is to analyze the function $y=|x|$. 2. The absolute value function $|x|$ is defined as: $$|x|=\begin{cases} x & \text{if } x \geq 0 \\ -x & \text{if } x < 0 \end{cases}$$ This means the output is always non-negative regardless of the input. 3. To understand the graph and behavior: - For $x \geq 0$, $y=x$ which is a straight line through the origin with slope 1. - For $x < 0$, $y=-x$ which is a straight line through the origin with slope -1. 4. The function is continuous everywhere and has a sharp corner at $x=0$. 5. The intercept is at the origin $(0,0)$. 6. The function has no extrema because it is V-shaped and the minimum value is at $y=0$ when $x=0$. Final answer: The function $y=|x|$ forms a V-shaped graph with vertex at the origin, composed of two linear pieces with slopes 1 and -1.