The function $y = 3|x|$ is an absolute value function. Its general form is $y = a|x|$, where $a$ controls the steepness of the graph. For $y = 3|x|$, the graph forms a V-shape with its vertex at the origin (0, 0), since there is no horizontal or vertical shift.

Let's break it down:

• Vertex: The vertex of the absolute value function $y = 3|x|$ is at the origin, (0, 0).
• Slope: The slope of the lines forming the V-shape is 3, meaning the graph rises steeply (3 units up for every 1 unit right or left from the vertex).

Would you like me to provide further details or a step-by-step guide for plotting? Here are five questions you can explore next:

1. How do transformations (shifting) affect the graph of $y = |x|$?
2. What is the difference between a graph of $y = 3|x|$ and $y = |x|$?
3. How can you solve for $x$ if given a specific $y$ value in $y = 3|x|$?
4. How does changing the coefficient of $|x|$ affect the graph?
5. How would the graph look if we added or subtracted a constant to $y = 3|x|$?

Tip: For absolute value functions, the vertex is the turning point where the graph changes direction.