Scaling of Functions: What is the Math Notation?

In summary, the conversation discusses the confusion around the notation "f(cx)" which represents a value of a function rather than a function itself. It also brings up the concept of a new function, g, defined by g(x) = f(cx), which can have a different graph depending on the value of c. This can be useful in engineering and transforms, but there is some ambiguity in the notation used.
  • #1
mmwave
647
2
In another thread Hallsofivy wrote

I think you are confusing things by always talking about "the function f(cx)". f(cx) does not represent a function, it represents a value of a function. f(x), f(y), f(cx) all refer to the same function, f.
-------------------------------------
Not wanting to hijack someone else's thread I've started this to discuss the following:

I understand that in all cases f( ) is the same function. But if c is greater than one a graph of f(cx) is 'skinnier' than f(x) and when c is less than one f(cx) is 'wider' than f(x). In engineering these are useful tools especially in transforms. x here is the independent variable not a single value. Maybe mathematicians use a different notation to discuss this concept?

Also, if f() is linear function then
f(cx) = c * f(x) for any x and
f(a+b) = f(a) + f(b)
 
Mathematics news on Phys.org
  • #2
You're implicitly defining a new function, g, given by:

g(x) := f(cx)

and it is the graph of this new function, g, that can be "skinnier" or "wider" than the graph of f.


Because of the common abuses of notation, there is some ambiguity in what precisely is meant.
 
  • #3
for any a and b.


The scaling of functions is a mathematical concept that involves changing the independent variable in a function. This can be represented using mathematical notation, specifically using the "f(cx)" notation. In this notation, "f" represents the function, "x" represents the independent variable, and "c" represents the scaling factor.

For example, if we have a function f(x) = x^2, and we want to scale it by a factor of 2, we would write it as f(2x) = (2x)^2 = 4x^2. This means that for any given value of x, the function will now output a value that is 4 times greater than the original function.

Similarly, if we want to scale the function by a factor of 1/2, we would write it as f(1/2x) = (1/2x)^2 = 1/4x^2. This means that for any given value of x, the function will now output a value that is 1/4 of the original function.

This notation is useful in engineering and other fields because it allows us to easily manipulate and analyze functions. For example, if we have a complex function and we want to see how it changes when we scale the independent variable, we can simply use the "f(cx)" notation to make the necessary calculations.

It is important to note that "f(cx)" does not represent a different function, but rather a scaled version of the original function. This means that all the properties and characteristics of the original function still apply, such as linearity and the ability to apply operations like addition and subtraction.

In summary, the notation "f(cx)" represents the scaling of a function by a factor of "c" on the independent variable "x". It is a useful tool in mathematics and other fields for analyzing and manipulating functions.
 

What is scaling of functions?

Scaling of functions refers to the process of changing the size or magnitude of a mathematical function. This can involve multiplying or dividing the function by a constant or changing the independent or dependent variables.

What is the math notation used for scaling of functions?

The most common notation used for scaling of functions is the use of a constant multiplier, represented by the letter "a", outside of the function. For example, the function f(x) can be scaled by a factor of 2 by writing 2f(x).

How does scaling affect the graph of a function?

Scaling of a function can affect the graph in different ways, depending on the type of function and the scaling factor used. It can result in a change in the slope, intercept, or curvature of the graph.

Can any function be scaled?

Yes, any mathematical function can be scaled, as long as the scaling factor is applied consistently to all parts of the function.

Why is scaling of functions important in science?

Scaling of functions is important in science because it allows us to manipulate and analyze data in a more meaningful way. It can help us understand relationships between variables and make predictions based on different scaling factors.

Similar threads

  • General Math
Replies
7
Views
852
  • General Math
Replies
12
Views
1K
Replies
2
Views
717
  • General Math
Replies
23
Views
1K
  • General Math
Replies
7
Views
1K
Replies
2
Views
786
Replies
6
Views
916
  • General Math
Replies
4
Views
915
  • General Math
Replies
5
Views
1K
Replies
1
Views
1K
Back
Top