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).