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graph transformation c2

What would a graph transformation of y =(4-x) look like on a x^2 graph?
Original post by Kolasinac138
What would a graph transformation of y =(4-x) look like on a x^2 graph?


I'm assuming that you're asking that if

f(x)=x2f(x)=x^2

then what f(4x)f(4-x) will look like.

Well, recall the following

f(x+a)f(x+a) represents a translation (i.e movement) by -a along the x axis.

f(x)f(-x) represents a reflection in the y axis.

You know what f(x)=x2f(x)=x^2 looks like, so first use one of the above to get a negative inside the bracket, and then think about what the 4 means.

It may help to write (4x)(4-x) as (x+4)(-x+4)
Reply 2
So it's a reflection in the y axis then movement of 4 units along the x?
Original post by Kolasinac138
So it's a reflection in the y axis then movement of 4 units along the x?


Remember, I said that f(x+a)f(x+a) means a movement of -a along the x axis. Other than that, you're right.
(edited 10 years ago)
Reply 4
Original post by Indeterminate
Not quite. Remember, I said that f(x+a)f(x+a) means a movement of -a along the x axis. Other than that, you're right.


A reflection in the y-axis means nothing however, so it's a movement of 4 units to the left?
Original post by Kolasinac138
A reflection in the y-axis means nothing however, so it's a movement of 4 units to the left?


You were right in the first place because of the negative sign
(edited 10 years ago)
Reply 6
Original post by Indeterminate
You were right in the first place because of the negative sign

What about this graph

Original post by Kolasinac138
What about this graph




The part that was originally below the x axis has been reflected in the x axis.

We call this

f(x)|f(x)|
(edited 10 years ago)
Reply 8
Original post by Indeterminate
The part that was originally below the x axis has been reflected in the x axis.

We call this

f(x)|f(x)|

I meant, what would f(2-x) look like here
Original post by Kolasinac138
I meant, what would f(2-x) look like here


Reflection in the y axis, as before, and then the the movement by 2 along the x axis.

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