Question

graph this function:
y = |3x|
click to plot the vertex first.

Explanation:

Step1: Find the vertex of \( y = |3x| \)

The general form of an absolute - value function is \( y=a|x - h|+k \), and its vertex is at \( (h,k) \). For the function \( y = |3x|=3|x| = 3|x - 0|+0 \), by comparing with the general form, we can see that \( h = 0 \) and \( k = 0 \). So the vertex of the function \( y=|3x| \) is at the point \( (0,0) \).

Step2: Find other points to graph the function

We can choose some values of \( x \) and find the corresponding values of \( y \).

• When \( x = 1 \), \( y=|3\times1| = 3 \), so we have the point \( (1,3) \).
• When \( x=- 1 \), \( y=|3\times(- 1)|=3 \), so we have the point \( (-1,3) \).
• When \( x = 2 \), \( y=|3\times2| = 6 \), so we have the point \( (2,6) \).
• When \( x=-2 \), \( y=|3\times(-2)| = 6 \), so we have the point \( (-2,6) \).

To graph the function, we first plot the vertex \( (0,0) \), and then plot the other points we found (like \( (1,3) \), \( (-1,3) \), \( (2,6) \), \( (-2,6) \)) and draw two rays from the vertex. One ray goes through the points with \( x\geq0 \) (e.g., \( (1,3) \), \( (2,6) \)) and the other ray goes through the points with \( x < 0 \) (e.g., \( (-1,3) \), \( (-2,6) \)).

Answer:

The vertex of the function \( y = |3x| \) is at \( (0,0) \). To complete the graph, plot additional points as calculated (e.g., \( (1,3) \), \( (-1,3) \), \( (2,6) \), \( (-2,6) \)) and draw the two rays of the absolute - value graph from the vertex.