Graph y = √(x + 1) + 2 from y = √x Step by Step

Step by step

The question

Question: graph y = √(x + 1) + 2 from y = √x.

y = √x + 1 + 2

We know the graph of y = √x.

It is half a U, lying on its side.

we know: y = √x

1 Read the changes

Inside, next to x, we have + 1.

x = −1 makes the inside 0.

So the start point moves to x = −1: left 1.

x + 1 inside → left 1

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

So the graph moves up 2.

+ 2 outside → up 2

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.

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 1.

Then up 2.

(0, 0) goes to (−1, 2).

(1, 1) goes to (0, 3).

(4, 2) goes to (3, 4).

4 Draw the new graph

Join the new points with the same shape.

This is y = √(x + 1) + 2.

5 Check

Let's check.

Put x = −1 in the new rule.

We get y = 2: the point (−1, 2) we drew.

x = −1: y = √−1 + 1 + 2 = √0 + 2 = 0 + 2

= 2

And x = 3 gives y = 4: the point (3, 4).

x = 3: y = √3 + 1 + 2 = √4 + 2 = 2 + 2 = 4

Let's look back.

First: read the changes.

Then: start from y = √x.

Then: move the points.

Then: draw the new graph.

Last: check.

Answer