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Transformation Of Functions

Draw the graph of y=f(x) where f(x)=x^2

Describe the transformation which maps y=f(x) to y=f(x-2)

For this I would basically have to draw the graph x^2 and move the graph 2 places to the right.

The thing is that I don't understand why are we moving the vertex two places to the right.
(edited 11 years ago)
Reply 1
Avatar for TenOfThem
TenOfThem
18
f(0) = 0

In the original graph x=0 gives f(0)
In the second graph x=2 gives f(0)
Reply 2
Avatar for zed963
zed963
OP
16
Original post by TenOfThem
f(0) = 0

In the original graph x=0 gives f(0)
In the second graph x=2 gives f(0)


I'm not following.

Why are you doing x=2 and what are you trying to show by f(x)=0
Reply 3
Avatar for TenOfThem
TenOfThem
18
Original post by zed963
I'm not following.

Why are you doing x=2 and what are you trying to show by f(x)=0


You asked why the vertex moved 2 places to the right

The vertex of the original graph is (0,0)

The vertex of the translated graph is (2,0)
Reply 4
Avatar for zed963
zed963
OP
16
Are you trying to say that to make x=0 what do I need to do to make it 0 so in this case add 2
Reply 5
Avatar for TenOfThem
TenOfThem
18
Original post by zed963
Are you trying to say that to make x=0 what do I need to do to make it 0 so in this case add 2


no
I am saying that to get the vertex in the transformed graph x=2

f(2-2) = 0
Reply 6
Avatar for zed963
zed963
OP
16
Original post by TenOfThem
no
I am saying that to get the vertex in the transformed graph x=2

f(2-2) = 0


Understood.
Reply 7
Avatar for zed963
zed963
OP
16
So how do I know which one I should choose for example if I was shown a graph and it told me to state the function and I had two choices to choose from which One would I choose.

So if I had f(-x) or -f(x)

What determines which one I choose
Reply 8
Avatar for TenOfThem
TenOfThem
18
Original post by zed963
So how do I know which one I should choose for example if I was shown a graph and it told me to state the function and I had two choices to choose from which One would I choose.

So if I had f(-x) or -f(x)

What determines which one I choose


Wether the x has changed [f(-x)] or the y has changed [-f(x)]

The former transforms parallel to the x-axis whereas the latter transforms parallel to the y-axis

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