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

Step by step

The question

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

y = √x − 2 + 1

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 − 2.

x = 2 makes the inside 0.

So the start point moves to x = 2: right 2.

x − 2 inside → right 2

Outside, at the end, + 1 adds 1 to every y.

So the graph moves up 1.

+ 1 outside → up 1

Careful!

Inside, it goes the opposite way to the sign.

Careful: − 2 inside goes right, not left

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 right 2.

Then up 1.

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

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

(4, 2) goes to (6, 3).

4 Draw the new graph

Join the new points with the same shape.

This is y = √(x − 2) + 1.

5 Check

Let's check.

Put x = 2 in the new rule.

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

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

And x = 6 gives y = 3: the point (6, 3).

x = 6: y = √6 − 2 + 1 = √4 + 1 = 2 + 1 = 3

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