Graph y = -√x + 3 from y = √x Step by Step

Step by step

The question

Question: graph y = −√x + 3 from y = √x.

y = −√x + 3

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

Outside, at the end, + 3 adds 3 to every y.

So the graph moves up 3.

+ 3 outside → up 3

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 up 3.

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

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

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

4 Draw the new graph

Join the new points with the same shape, flipped.

This is y = −√x + 3.

5 Check

Let's check.

Put x = 0 in the new rule.

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

x = 0: y = −√0 + 3 = 0 + 3 = 3

And x = 4 gives y = 1: the point (4, 1).

x = 4: y = −√4 + 3 = −2 + 3 = 1

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