Graph y = 2x^3 from y = x^3

Step by step

The question

Question: graph y = 2x³ from y = x³.

We know the graph of y = x³.

It is an S shape.

1 Read the changes

The 2 in front makes every y 2 times as big.

The graph gets steeper.

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

(−1, −1) goes to (−1, −2).

(0, 0) stays where it is.

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

4 Draw the new graph

Join the new points with the same shape.

This is y = 2x³.

5 Check

Let's check.

Put x = 0 in the new rule.

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