graph transformations

I know how you apply a single graph transformation e.g. 2f(x). But how do I know in which order I apply multiple graph transformations?

Say if I have on a graph called f(x) the point (60, 10). I then apply the graph transformation of 2f(4x+3)+1. Does the new x coordinate become (60-3)/4? Or does it become (60/4)-3? Same goes with the new y coordinate. Does the new y coordinate become (10 X 2)+1? Or does it become (10+1)(2)?

Thanks.

Reply 1

Indeterminate

3

Original post by krisshP

I know how you apply a single graph transformation e.g. 2f(x). But how do I know in which order I apply multiple graph transformations?

Say if I have on a graph called f(x) the point (60, 10). I then apply the graph transformation of 2f(4x+3)+1. Does the new x coordinate become (60-3)/4? Or does it become (60/4)-3? Same goes with the new y coordinate. Does the new y coordinate become (10 X 2)+1? Or does it become (10+1)(2)?

Thanks.

You can apply them in any order, but it's generally simpler to consider the f bit first :smile:

Be careful with 2f(4x+3) + 1.

f(ax)

multiplies the x coordinates by

\frac{1}{a}

af(x)

multiplies the y coordinates by a.

f(x+a)

moves the grpah -a in the x direction.

f(x) + a

moves the graph a in the y-direction.

Reply 2

Bixel

5

As far as I've learnt, graph transformations can be applied in any order, do whatever you feel is comfortable!
I normally start with the 'stretches' first, then followed by the translations.

Reply 3

aznkid66

1

PEMDAS for y, reverse PEMDAS for x.

Note that, in this way, you would be doing stretches first for y and translations first for x.

If you were doing it in the reverse order, then you would have to change the constants of translation by expressing the transformation as the following:

2f(4x+3)+1=2(f(4(x+3/4))+1/2)

(edited 11 years ago)

Reply 4

aznkid66

1

Lol, I don't see why I got negged. Clearly (60-3)/4 does not equal (60/4)-3, and so OP needs to understand that ordering the transformations differently will change to what extent each transformation should affect the value.

Reply 5

krisshP

OP

14

Original post by Indeterminate

You can apply them in any order, but it's generally simpler to consider the f bit first :smile:

But you get different values. See my first post on this thread. Look at the example there. How would you do that transformation of the point then?

Reply 6

aznkid66

1

Original post by krisshP

But you get different values. See my first post on this thread. Look at the example there. How would you do that transformation of the point then?

Hey, I posted stuff too. :'(

Let's look at y=f(4x+3)=f(4(x+3/4))

You can interpret this as a shift of 3 and a stretch of 1/4 or as a stretch of 1/4 and a shift of 3/4.

Follow the order of the operations/transformations.

graph transformations

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