Step by step
The question
Question: graph y = |x| − 2 from y = |x|.
y = |x| − 2
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
Outside, at the end, − 2 takes 2 away from every y.
So the graph moves down 2.
− 2 outside → down 2
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
Move it down 2.
The new corner is (0, −2).
4 Draw the new graph
The shape stays the same.
From the corner, 1 right, 1 up.
And 1 left, 1 up.
Join them with the same V.
This is y = |x| − 2.
5 Check
Let's check.
Put x = 0 in the new rule.
We get y = −2: the corner (0, −2).
x = 0: y = |0| − 2 = 0 − 2 = −2
And x = 1 gives y = −1: the point (1, −1) we drew.
x = 1: y = |1| − 2 = 1 − 2 = −1
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
− 2 outside → down 2