Graph y = -1/(x - 1) from y = 1/x Step by Step

Step by step

The question

Question: graph y = −1/(x − 1) from y = 1/x.

y = −1x − 1

We know the graph of y = 1/x.

It is two curves, one in each corner.

we know: y = 1/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

Inside, next to x, we have − 1.

x = 1 makes the inside 0.

So the center moves to x = 1: right 1.

x − 1 inside → right 1

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 = 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 right 1.

(−1, −1) goes to (0, 1).

(1, 1) goes to (2, −1).

4 Draw the new graph

1/x never touches the axes.

Those two lines move too.

Now it never touches x = 1 and y = 0.

Join the new points with the same shape, flipped.

This is y = −1/(x − 1).

5 Check

Let's check.

Put x = 2 in the new rule.

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

x = 2: y = −12 − 1 = −11 = −1

And x = 0 gives y = 1: the point (0, 1).

x = 0: y = −10 − 1 = −1−1 = 1

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.

Answer