Step by step
The question
Question: graph y = one third times |x|, − 2, from y = |x|.
We know the graph of y = |x|.
It is a V.
1 Read the changes
The one third in front makes every y one third as big.
Smaller y's: the graph gets wider and flatter.
Careful!
A number bigger than 1 makes it narrower.
A number between 0 and 1 makes it wider.
Outside, at the end, − 2 takes 2 away from every y.
So the graph moves down 2.
2 Start from y = |x|
Draw the grid.
Draw y = |x| first.
It goes through (−3, 3), (0, 0) and (3, 3).
3 Shrink the y's
(−3, 3): one third of 3 is 1.
It goes to (−3, 1).
(0, 0) stays: one third of 0 is 0.
(3, 3): one third of 3 is 1.
It goes to (3, 1).
4 Move the corner
The corner moves down 2.
Every point moves the same way.
The new points: (−3, −1), (0, −2) and (3, −1).
5 Draw the new graph
Join them with the same shape, wider.
This is the new graph.
6 Check
Let's check: put x = 3 in the new rule.
One third of 3 is 1, minus 2 is −1.
We get the point (3, −1).
It works!
Let's look back.
First: read the changes.
Then: start from y = |x|.
Then: shrink the y's.
Then: move the corner.
Then: draw the new graph.
Last: check.