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 is inside, with x.

It changes the sign of every x.

Right becomes left.

So the graph flips over the y-axis.

−x inside → flip over the y-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, 4).

(4, 2) goes to (−4, 5).

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 = 0 + 3 = 3

And x = −4 gives y = 5: the point (−4, 5).

x = −4: y = √−(−4) + 3 = √4 + 3 = 2 + 3 = 5

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