Graph y = 1/x - 3 from y = 1/x

Step by step

The question

Question: graph y = 1/x − 3 from y = 1/x.

We know the graph of y = 1/x.

It is two curves, one in each corner.

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 = 1/x

Draw the grid.

Draw y = 1/x first.

It goes through (−1, −1) and (1, 1).

3 Move the points

The center (0, 0) moves down 3.

(−1, −1) goes to (−1, −4).

(1, 1) goes to (1, −2).

4 Draw the new graph

1/x never touches the axes.

Those two lines move too.

Now it never touches x = 0 and y = −3.

Join the new points with the same shape.

This is y = 1/x − 3.

5 Check

Let's check.

Put x = 1 in the new rule.

We get y = −2: the point (1, −2) we drew.

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

Let's look back.

First: read the changes.

Then: start from y = 1/x.

Then: move the points.

Then: draw the new graph.

Last: check.