1. The problem is to understand and graph the function $y = |x - 2|$. 2. The absolute value function $|x - 2|$ represents the distance of $x$ from 2 on the number line. 3. The formula for absolute value is: $$|a| = \begin{cases} a & \text{if } a \geq 0 \\ -a & \text{if } a < 0 \end{cases}$$ 4. Applying this to $y = |x - 2|$, we get: $$y = \begin{cases} x - 2 & \text{if } x - 2 \geq 0 \\ -(x - 2) & \text{if } x - 2 < 0 \end{cases}$$ which simplifies to: $$y = \begin{cases} x - 2 & \text{if } x \geq 2 \\ -x + 2 & \text{if } x < 2 \end{cases}$$ 5. This means the graph is a V-shaped function with vertex at $(2,0)$. 6. For $x \geq 2$, the graph is the line $y = x - 2$. 7. For $x < 2$, the graph is the line $y = -x + 2$. 8. The graph intercepts the x-axis at $x=2$ and the y-axis at $y=2$. 9. This function has a minimum (extremum) at the vertex $(2,0)$. Final answer: The graph of $y = |x - 2|$ is a V-shaped graph with vertex at $(2,0)$, composed of two lines $y = x - 2$ for $x \geq 2$ and $y = -x + 2$ for $x < 2$.