Graph y = -1/x - 2 from y = 1/x Step by Step

Step by step

The question

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

y = −1x − 2

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

Outside, at the end, − 2 takes 2 away from every y.

So the graph moves down 2.

− 2 outside → down 2

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 down 2.

(−1, −1) stays where it is.

(1, 1) goes to (1, −3).

4 Draw the new graph

1/x never touches the axes.

Those two lines move too.

Now it never touches x = 0 and y = −2.

Join the new points with the same shape, flipped.

This is y = −1/x − 2.

5 Check

Let's check.

Put x = 1 in the new rule.

We get y = −3: the point (1, −3) we drew.

x = 1: y = −11 − 2 = −1 − 2 = −3

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

x = −1: y = −1−1 − 2 = 1 − 2 = −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