Graph y = 1/(x + 3) from y = 1/x Step by Step

Step by step

The question

Question: graph y = 1/(x + 3) from y = 1/x.

y = 1x + 3

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 + 3.

x = −3 makes the inside 0.

So the center moves to x = −3: left 3.

x + 3 inside → left 3

Careful!

Inside, it goes the opposite way to the sign.

Careful: + 3 inside goes left, not right

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 left 3.

(−1, −1) goes to (−4, −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 = −3 and y = 0.

Join the new points with the same shape.

This is y = 1/(x + 3).

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 = 1−2 + 3 = 11 = 1

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

x = −4: y = 1−4 + 3 = 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