Graph y = |x| + 2 from y = |x|

Step by step

The question

Question: graph y = |x| + 2 from y = |x|.

We know the graph of y = |x|.

It is a V, with its corner at (0, 0).

1 Read the changes

Outside, at the end, + 2 adds 2 to every y.

So the graph moves up 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 up 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).

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.