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

Step by step

The question

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

y = −√x − 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

The minus in front changes the sign of every y.

Up becomes down.

So the graph flips over the x-axis.

− in front → flip over the x-axis

Inside, next to x, we have − 1.

x = 1 makes the inside 0.

So the start point moves to x = 1: right 1.

x − 1 inside → right 1

Careful!

A minus inside flips left and right.

A minus outside flips up and down.

Careful: inside → left-right, outside → up-down

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 1.

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

(1, 1) goes to (2, −1).

(4, 2) goes to (5, −2).

4 Draw the new graph

Join the new points with the same shape, flipped.

This is y = −√(x − 1).

5 Check

Let's check.

Put x = 1 in the new rule.

We get y = 0: the point (1, 0) we drew.

x = 1: y = −√1 − 1 = −√0 = 0

And x = 5 gives y = −2: the point (5, −2).

x = 5: y = −√5 − 1 = −√4 = −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.

Answer