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The question asks for the equation of a function \( g(x) \) that shifts the graph of \( f(x) = |x| \) 4 units to the right and 3 units up.

To achieve these transformations:

- Shifting the graph **right by 4 units**: This transformation is achieved by replacing \( x \) with \( (x - 4) \). So, \( f(x) = |x| \) becomes \( f(x - 4) = |x - 4| \).
- Shifting the graph **up by 3 units**: This is done by adding 3 to the entire function. So, \( f(x) = |x| \) becomes \( f(x) + 3 = |x| + 3 \).

Therefore, the equation for the function \( g(x) \) is:
\[
g(x) = |x - 4| + 3
\]

This is the function that shifts the graph of \( f(x) = |x| \) right by 4 units and up by 3 units.

Would you like further explanation or details?

Here are 5 related questions you might find useful:
1. How does shifting the graph left instead of right affect the equation?
2. What happens if we shift the graph down instead of up?
3. How can we combine vertical stretching or compression with this transformation?
4. What is the general form of transformations for absolute value functions?
5. How do horizontal stretches or compressions affect the graph?

**Tip**: To shift a graph left or right, adjust the value inside the function's argument (inside absolute value, parentheses, etc.). To shift up or down, modify the entire function outside the argument.

The graph of f(x) = |x| is given below. Write the equation of a function g(x) which would shift the graph of f(x) right 4 units and up 3 units.

Learn how to shift the graph of the absolute value function f(x) = |x| right by 4 units and up by 3 units. This example covers key concepts in graph transformations and is suitable for students in Grades 8-10.

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