Step by step
The question
Question: graph y = 2√x + 1 from y = √x.
y = 2√x + 1
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 2 in front makes every y 2 times as big.
The graph gets steeper.
2 in front → every y × 2
Outside, at the end, + 1 adds 1 to every y.
So the graph moves up 1.
+ 1 outside → up 1
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
The start point (0, 0) moves up 1.
(0, 0) goes to (0, 1).
(1, 1) goes to (1, 3).
(4, 2) goes to (4, 5).
4 Draw the new graph
Join the new points with the same shape.
This is y = 2√x + 1.
5 Check
Let's check.
Put x = 0 in the new rule.
We get y = 1: the point (0, 1) we drew.
x = 0: y = 2√0 + 1 = 2 × 0 + 1 = 1
And x = 4 gives y = 5: the point (4, 5).
x = 4: y = 2√4 + 1 = 2 × 2 + 1 = 5
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
+ 1 outside → up 1