There is a function h that has been shifted 3 unit up and 1 unit left from the function f(x) = | x-1| + 2. sketch both the function

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.

There is a function h that has been shifted 3 units up and 1 unit left from the function f(x) = |x - 1| + 2. Sketch both the functions.

Explore the transformation of absolute value functions by graphing f(x) = |x - 1| + 2 and its shifted version h(x) = |x| + 5. Learn how shifts affect the vertex and shape of the graph. Suitable for students in Grades 8-10.

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