Here is the graph of the two functions:

• The blue line represents $f(x) = |x - 1| + 2$, which has a vertex at $(1, 2)$.
• The red dashed line represents $h(x) = |x| + 5$, which is the result of shifting $f(x)$ 1 unit left and 3 units up, and has its vertex at $(0, 5)$.

Would you like more details or have any specific questions?

Here are 5 related questions to explore further:

1. How would the graph change if the function was shifted 2 units down instead of up?
2. What happens to the graph if we reflect it over the x-axis?
3. How does the slope of the absolute value function affect the shape of the graph?
4. How do different horizontal shifts affect the domain and range of the function?
5. What is the effect of a vertical stretch on an absolute value function?

Tip: Always identify the vertex of an absolute value function first, as it helps you understand the transformations more easily.