Graph the equation of y = |x| translated 3 units up.
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The equation \( y = |x| \) represents the graph of an absolute value function, which has a "V" shape with the vertex at the origin (0, 0).

When the function is translated 3 units up, the new equation becomes:

\[
y = |x| + 3
\]

### Graph Explanation:

- The graph of \( y = |x| \) has its vertex at (0, 0).
- The translation 3 units up means the entire graph is shifted vertically upward by 3 units.
- The new vertex will be at (0, 3), and the "V" shape remains the same.
- For \( x = 0 \), \( y = 3 \), and for \( x = \pm 1 \), \( y = 4 \), and so on.

Would you like me to graph it for you, provide more details, or clarify any steps?

### Related questions:
1. How do you graph horizontal translations of absolute value functions?
2. What happens if we translate \( y = |x| \) down instead of up?
3. Can absolute value functions be reflected over the x-axis?
4. How does the slope of the "V" change if the equation becomes \( y = 2|x| \)?
5. What is the impact of adding constants inside the absolute value, like \( y = |x + 2| \)?

### Tip:
When translating graphs, vertical shifts affect only the y-coordinates of every point on the graph, while horizontal shifts affect the x-coordinates.

Graph the equation of y = |x| translated 3 units up.

Explore how to graph the equation y = |x| after translating it 3 units up. This problem demonstrates key concepts in algebra, such as absolute value functions and vertical shifts. Suitable for students in Grades 8-10.

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