Transformation of a function

In summary: Can you please clarify?In summary, the conversation discusses the transformation of a function from one coordinate system to another. It is questioned whether simply transforming the coordinates is enough or if the form of the function also needs to be considered. An example of a linear transformation is given, but it is acknowledged that there may be cases where this is not enough. There is some disagreement on whether knowing the form of the function is necessary for the transformation. One person gives an unclear example of a function, x2ey, and it is unclear what the question is.
  • #1
sadegh4137
72
0
consider we have function

f= f ( x , y )

that x and y are our coordinate system.
we know that x and y how transform to new coordinate system for example
x' and y'

here arises a question and that
how function f transform to new coordinate system?
 
Mathematics news on Phys.org
  • #2
g(x',y') = f(x(x',y'),y(x',y'))

Based on your description, this is all that one can say.
 
  • #3
can we say that the form of function can not change?

and for transform a function, its enough that we transform coordinates?

for example
consider have this function
exp( i kx - wt)

and we want to transform this under Galilean transformation can we put x and t exchange by x' and t', without form of function change?
 
  • #4
For the specific case you described, the form doesn't change. The transformation is linear, but there could be situations where that is not enough.
 
  • #5
it means you say for all transformation, it enough we transform x and y to x' and y' for example

without think to form of function

some people say it isn't enough beside this, we should know the form of function how will change.

it is true?
 
  • #6
Look at x2ey

It is not clear to me what you are trying to ask.
 

1. What is a transformation of a function?

A transformation of a function is a change in the form or appearance of a function without changing its underlying structure. It involves applying a set of rules or operations to a function to produce a new function with different graph characteristics.

2. What are the common types of transformations of a function?

The common types of transformations of a function include translations, reflections, dilations, and combinations of these. Translations shift the function horizontally or vertically, reflections flip the function across an axis, and dilations stretch or compress the function.

3. How do transformations affect the graph of a function?

Transformations can change the position, size, and orientation of the graph of a function. They can also affect the domain and range of the function. For example, a translation shifts the graph horizontally or vertically, while a reflection flips the graph across an axis.

4. What is the difference between a rigid transformation and a non-rigid transformation?

A rigid transformation is a transformation that preserves the size and shape of a function's graph. Examples include translations and reflections. A non-rigid transformation, on the other hand, changes the size or shape of the graph, such as dilations or combinations of transformations.

5. How can transformations be used to analyze and compare functions?

Transformations can be used to analyze and compare functions by visually identifying their similarities and differences. For instance, if two functions have the same initial shape but are shifted or stretched differently, this can indicate a relationship between the two functions. Transformations can also be used to simplify complex functions by breaking them down into smaller, more manageable parts.

Similar threads

Replies
2
Views
1K
Replies
17
Views
2K
  • General Math
Replies
11
Views
235
Replies
1
Views
677
  • General Math
Replies
25
Views
2K
Replies
1
Views
592
  • General Math
Replies
5
Views
959
Replies
9
Views
1K
  • Differential Geometry
Replies
9
Views
332
  • General Math
Replies
2
Views
666
Back
Top