Step by step
The question
Question: graph y = 3|x| from y = |x|.
y = 3|x|
We know the graph of y = |x|.
It is a V, with its corner at (0, 0).
we know: y = |x|
1 Read the changes
The 3 in front makes every y 3 times as big.
The V gets narrower.
3 in front → every y × 3
2 Start from y = |x|
Draw the grid.
The x-axis goes across.
The y-axis goes up and down.
They meet at 0.
That point is called the origin.
Draw y = |x| first.
Its corner is at (0, 0).
3 Move the corner
The corner stays at (0, 0).
4 Draw the new graph
Every y is 3 times as far.
From the corner, 1 right, 3 up.
And 1 left, 3 up.
Join them with a narrower V.
This is y = 3|x|.
5 Check
Let's check.
Put x = 0 in the new rule.
We get y = 0: the corner (0, 0).
x = 0: y = 3|0| = 3 × 0 = 0
And x = 1 gives y = 3: the point (1, 3) we drew.
x = 1: y = 3|1| = 3 × 1 = 3
Let's look back.
First: read the changes.
Then: start from y = |x|.
Then: move the corner.
Then: draw the new graph.
Last: check.
Answer
3 in front → every y × 3