Graph y = 1/(x - 2) + 1 from y = 1/x Step by Step

Step by step

The question

Question: graph y = 1/(x − 2) + 1 from y = 1/x.

y = 1x − 2 + 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

Inside, next to x, we have − 2.

x = 2 makes the inside 0.

So the center moves to x = 2: right 2.

x − 2 inside → right 2

Outside, at the end, + 1 adds 1 to every y.

So the graph moves up 1.

+ 1 outside → up 1

Careful!

Inside, it goes the opposite way to the sign.

Careful: − 2 inside goes right, not left

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 2.

Then up 1.

(−1, −1) goes to (1, 0).

(1, 1) goes to (3, 2).

4 Draw the new graph

1/x never touches the axes.

Those two lines move too.

Now it never touches x = 2 and y = 1.

Join the new points with the same shape.

This is y = 1/(x − 2) + 1.

5 Check

Let's check.

Put x = 3 in the new rule.

We get y = 2: the point (3, 2) we drew.

x = 3: y = 13 − 2 + 1 = 11 + 1 = 1 + 1 = 2

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

x = 1: y = 11 − 2 + 1 = 1−1 + 1 = −1 + 1 = 0

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