Move y = |x| to y = 2|x + 1| Step by Step

Step by step

The question

Question: graph y = 2|x + 1| from y = |x|.

y = 2|x + 1|

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 2 in front makes every y 2 times as big.

The V gets narrower.

2 in front → every y × 2

Inside, next to x, we have + 1.

x = −1 makes the inside 0.

So the corner moves to x = −1: left 1.

x + 1 inside → left 1

Careful!

Inside, it goes the opposite way to the sign.

Careful: + 1 inside goes left, not right

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 left 1.

The new corner is (−1, 0).

4 Draw the new graph

Every y is 2 times as far.

From the corner, 1 right, 2 up.

And 1 left, 2 up.

Join them with a narrower V.

This is y = 2|x + 1|.

5 Check

Let's check.

Put x = −1 in the new rule.

We get y = 0: the corner (−1, 0).

x = −1: y = 2|−1 + 1| = 2|0| = 2 × 0 = 0

And x = 0 gives y = 2: the point (0, 2) we drew.

x = 0: y = 2|0 + 1| = 2|1| = 2 × 1 = 2

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