Write an **equation** of an absolute value graph that has been shifted up 3 units and right 2 units.

The general form of an absolute value function is:

\[
f(x) = |x - h| + k
\]

Where:
- \( h \) represents the horizontal shift (right if positive, left if negative).
- \( k \) represents the vertical shift (up if positive, down if negative).

Given that the graph is shifted up 3 units and right 2 units, the equation becomes:

\[
f(x) = |x - 2| + 3
\]

Would you like further explanation, or have any questions?

Here are 5 related questions to deepen your understanding:
1. How would the equation change if the graph were shifted left 4 units and down 5 units?
2. What does the graph of \( f(x) = |x| \) look like before any shifts?
3. How would you reflect an absolute value graph across the x-axis?
4. How do you find the vertex of the graph from the equation \( f(x) = |x - h| + k \)?
5. What happens to the shape of the graph if you multiply the absolute value by a constant?

**Tip:** Horizontal shifts are always in the opposite direction of the sign in the equation (i.e., \( x - 2 \) means shifting **right** by 2 units).

Write an equation of an absolute value graph that has been shifted up 3 units and right 2 units.

Learn how to write the equation of an absolute value function that has been shifted up 3 units and right 2 units. This problem covers key algebraic concepts, including graph transformations of absolute value functions, and is suitable for students in Grades 7-9.

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