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.