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reallylongnickname

Member

Registered: 2011-03-30

Posts: 50

Transformation of exp func

If I have a function for example:

-Where did the  +10 come from?
-what is the rule for getting the x value?
-where did the the (x-3) come from?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Transformation of exp func

Hi reallylongnickname;

Welcome to the forum.

Did you copy the entire problem?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

reallylongnickname

Member

Registered: 2011-03-30

Posts: 50

Re: Transformation of exp func

Hello, here is what the original Q askes, but I'm not expecting to go through all this. I'm looking for the equation part.

-state the transformations that must be applied to f(x)
-state the y-int and the eq of asymptote
-sketch the new function
-state domain and range

Last edited by reallylongnickname (2011-04-14 21:43:07)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Transformation of exp func

hi reallylongnickname

When x = 0, y = 1.

As x tends to - infinity y tends to 0 so that's your asymptote.

I have no idea about transformations.  I think you could apply practically any transform to the graph / function so what is this part of the question on about?  Have you got a known example to show what this might mean?

That messes up the new function part too, so on to the end.

For the original function I suppose you could choose  x is any real and the range is y > 0.

Sorry about the rest.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

reallylongnickname

Member

Registered: 2011-03-30

Posts: 50

Re: Transformation of exp func

Ok, disregard the +10 for now. It may not belong there.
We know that

is going to be outside the brackets. So,

and the

is going to be what is inside the brackets. So

My Q is about

. How did it go from being

to being

then finaly,

Last edited by reallylongnickname (2011-04-14 23:27:55)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Transformation of exp func

hi reallylongnickname

I think I've worked out what you are studying and from that, what your question means.

You start with a 'simple' graph such as

and then say how that graph is transformed when a more complicated formula is substituted such as

Take the transforms one at a time.

(x-3)
On the original graph a certain value of x results in a certain y = f(x).

On the new graph 'x' has to be + three bigger to give the same 'y' so the new graph is the old one move 3 places right on the x axis.

2 x (....)
As the 'x' is going to be doubled, a value half of that on the original graph will give the same 'y' on the new graph.

After the function f is applied to these values of x, we get a transformed graph.

But now it is multiplied by -2

This will stretch it in the 'y' direction with scale factor x2 and reflect it in the x axis.

So altogether the original graph is moved right by 3, shrunk in the x direction by scale factor 1/2, stretched in the y direction by scale factor 2, and reflected in the x axis.

I've put a graph below showing the original, the translated graph in red, the shrunken graph in green and the stretched graph in blue.  I have left out the reflection because it was hard enough getting a useful scale for the first four without negative values as well.

Is that what you were after,

Bob

Last edited by Bob (2011-04-15 02:24:12)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob