Graph y = x^3 - 3 from y = x^3

Step by step

The question

Question: graph y = x³ − 3 from y = x³.

We know the graph of y = x³.

It is an S shape.

1 Read the changes

Outside, at the end, − 3 takes 3 away from every y.

So the graph moves down 3.

2 Start from y = x³

Draw the grid.

Draw y = x³ first.

It goes through (−1, −1), (0, 0) and (1, 1).

3 Move the points

The middle point (0, 0) moves down 3.

(−1, −1) goes to (−1, −4).

(0, 0) goes to (0, −3).

(1, 1) goes to (1, −2).

4 Draw the new graph

Join the new points with the same shape.

This is y = x³ − 3.

5 Check

Let's check.

Put x = 0 in the new rule.

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

And x = 1 gives y = −2: the point (1, −2).

Let's look back.

First: read the changes.

Then: start from y = x³.

Then: move the points.

Then: draw the new graph.

Last: check.