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sisyphus

Member

Registered: 2016-05-15

Posts: 26

Question about function transformations

Good day good people.

I have a function: f(x) = x^2
Its point:              (-2, 4)
Second function: g(x) = (x+2)^2 - 3
Its point:              (-4, 1)

So the second function is a transformation of the first function:

g(x) = (x+2)^2 - 3  =   f(x+2) - 3

I understand why -2 (x in point one) becomes -4 (x in point two):

x + 2 = -2
x = -4

Now i don't understand (conceptually) why 4 (y in point one) becomes 1 (y in point two). Since i have changed the input in the transformation function from x to (x+2), why doesn't the output reflect this change and i'm still left with 4, from which i then subtract 3? Shouldn't 4 become 16 (because i have -4 in my input now) from which i then subtract 3? I know the right sequence of actions here, i just don't understand why. I feel like i'm thinking about this in a completely wrong way.

Last edited by sisyphus (2016-05-23 02:53:44)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Question about function transformations

hi Sisyphus

You have said it's a transformation, so maybe it will help to ask what transformation?

Bob

---

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

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Question about function transformations

Your g(x)=f(x+2)-3; You can not make it f(x)-3;

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

sisyphus

Member

Registered: 2016-05-15

Posts: 26

Re: Question about function transformations

For some reason i was thinking about this whole problem algorithmically. This is how my thinking was going - i have a number as an input to the function, i change that number with +2 (i make an equation to find x), now i plug in the changed input into the function, which gives me a different output which i also change with -3. In the midst of it, it never occurred to me that i had to change the placement of the parabola in the cartesian plane by not changing it's dimensions. Looking at the graph of the side by side comparison helped me to at least start to understand what was it that i was trying to do here, i also had to look up what "translation vector" meant, so i probably skipped a topic somewhere, as this is the first time i heard about it. 

Thank you for the help guys, i'm still fuzzy about this whole function transformation thing, but the rays of light are starting to get through (i hope).

Last edited by sisyphus (2016-05-23 05:42:04)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Question about function transformations

Have a look here:

http://www.mathsisfun.com/geometry/translation.html

Bob

---

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

sisyphus

Member

Registered: 2016-05-15

Posts: 26

Re: Question about function transformations

Have a look here:

http://www.mathsisfun.com/geometry/translation.html

Bob

Already looked it up in google, but thanks!