Step by step
The question
Question: graph y = −|x| + 4 from y = |x|.
We know the graph of y = |x|.
It is a V, with its corner at (0, 0).
1 Read the changes
The minus in front turns every y into minus y.
So the V flips upside down.
Outside, at the end, + 4 adds 4 to every y.
So the graph moves up 4.
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 up 4.
The new corner is (0, 4).
4 Draw the new graph
The shape is flipped.
From the corner, 1 right, 1 down.
And 1 left, 1 down.
Join them with an upside-down V.
This is y = −|x| + 4.
5 Check
Let's check.
Put x = 0 in the new rule.
We get y = 4: the corner (0, 4).
And x = 1 gives y = 3: the point (1, 3) we drew.
Let's look back.
First: read the changes.
Then: start from y = |x|.
Then: move the corner.
Then: draw the new graph.
Last: check.