1. The problem is to analyze the function $h(x) = 3|x - 2|$. 2. The absolute value function $|x - 2|$ measures the distance of $x$ from 2 on the number line. 3. The function $h(x)$ multiplies this distance by 3, stretching the graph vertically by a factor of 3. 4. To understand $h(x)$, recall the definition of absolute value: $$|x - 2| = \begin{cases} x - 2 & \text{if } x \geq 2 \\ -(x - 2) & \text{if } x < 2 \end{cases}$$ 5. Therefore, $h(x)$ can be written as: $$h(x) = \begin{cases} 3(x - 2) & \text{if } x \geq 2 \\ 3(2 - x) & \text{if } x < 2 \end{cases}$$ 6. This means the graph has a "V" shape with its vertex at the point $(2,0)$. 7. For $x \geq 2$, the function increases linearly with slope 3. 8. For $x < 2$, the function decreases linearly with slope -3. 9. The vertex at $(2,0)$ is the minimum point of the function. Final answer: The function $h(x) = 3|x - 2|$ is a V-shaped graph with vertex at $(2,0)$, slopes 3 and -3 on either side, and is vertically stretched by a factor of 3 compared to $|x - 2|$.