Graph y = √(x + 3) from y = √x

Step by step

The question

Question: graph y = √(x + 3) from y = √x.

We know the graph of y = √x.

It is half a U, lying on its side.

1 Read the changes

Inside, next to x, we have + 3.

x = −3 makes the inside 0.

So the start point moves to x = −3: left 3.

Careful!

Inside, it goes the opposite way to the sign.

2 Start from y = √x

Draw the grid.

Draw y = √x first.

It goes through (0, 0), (1, 1) and (4, 2).

3 Move the points

The start point (0, 0) moves left 3.

(0, 0) goes to (−3, 0).

(1, 1) goes to (−2, 1).

(4, 2) goes to (1, 2).

4 Draw the new graph

Join the new points with the same shape.

This is y = √(x + 3).

5 Check

Let's check.

Put x = −3 in the new rule.

We get y = 0: the point (−3, 0) we drew.

And x = 1 gives y = 2: the point (1, 2).

Let's look back.

First: read the changes.

Then: start from y = √x.

Then: move the points.

Then: draw the new graph.

Last: check.