Step by step
The question
Question: graph y = −x³ from y = x³.
y = −x3
We know the graph of y = x³.
It is an S shape.
we know: y = x³
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
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 = x³
Draw the grid.
Draw y = x³ first.
It goes through (−1, −1), (0, 0) and (1, 1).
3 Move the points
(−1, −1) goes to (−1, 1).
(0, 0) stays where it is.
(1, 1) goes to (1, −1).
4 Draw the new graph
Join the new points with the same shape, flipped.
This is y = −x³.
5 Check
Let's check.
Put x = 0 in the new rule.
We get y = 0: the point (0, 0) we drew.
x = 0: y = −(0)3 = 0
And x = 1 gives y = −1: the point (1, −1).
x = 1: y = −(1)3 = −1
Let's look back.
First: read the changes.
Then: start from y = x³.
Then: move the points.
Then: draw the new graph.
Last: check.
Answer
− in front → flip over the x-axis