Graph this function:
y=3|x|
Click to plot the vertex first.'

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.

Graph this function: y=3|x| Click to plot the vertex first.

Learn how to graph the absolute value function y=3|x|. This guide covers the key concepts of absolute value functions, including identifying the vertex and understanding the slope of the graph. Suitable for students in Grades 8-10.

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