Step by step
The question
Question: graph y = one half times √x, from y = √x.
y = 12√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 one half in front makes every y one half as big.
Smaller y's: the graph gets wider and flatter.
12 in front → every y × 12
Careful!
A number bigger than 1 makes it narrower.
A number between 0 and 1 makes it wider.
Careful: a number between 0 and 1 in front: wider, not narrower
2 Start from y = √x
Draw the grid.
Draw y = √x first.
It goes through (0, 0) and (4, 2).
3 Shrink the y's
(0, 0) stays: one half of 0 is 0.
(4, 2): one half of 2 is 1.
It goes to (4, 1).
4 Draw the new graph
Join them with the same shape, wider.
This is the new graph.
5 Check
Let's check: put x = 4 in the new rule.
One half of 2 is 1.
We get the point (4, 1).
It works!
x = 4: y = 12√4 = 12 × 2 = 1
Let's look back.
First: read the changes.
Then: start from y = √x.
Then: shrink the y's.
Then: draw the new graph.
Last: check.
Answer
12 in front → every y × 12