Step by step
The question
Question: graph y = −√x from y = √x.
y = −√x
We know the graph of y = √x.
It is half a U, lying on its side.
we know: y = √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
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 = √x
Draw the grid.
Draw y = √x first.
It goes through (0, 0), (1, 1) and (4, 2).
3 Move the points
(0, 0) stays where it is.
(1, 1) goes to (1, −1).
(4, 2) goes to (4, −2).
4 Draw the new graph
Join the new points with the same shape, flipped.
This is y = −√x.
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 = 0
And x = 4 gives y = −2: the point (4, −2).
x = 4: y = −√4 = −2
Let's look back.
First: read the changes.
Then: start from y = √x.
Then: move the points.
Then: draw the new graph.
Last: check.
Answer
− in front → flip over the x-axis