Can we consider equations as functions?

  • Thread starter charliemagne
  • Start date
  • Tags
    Functions
In summary, the conversation discusses whether equations can be considered as functions. While some argue that equations are not actually functions, others believe that they are used to define or represent functions. The example of y=4x+1/f(x)=4x+1 is brought up as a potential function. Overall, it is concluded that the definition of a function as a set of ordered pairs is primarily used for studying functions in a set theoretic setting, and the semantics of whether an equation can be considered a function is not particularly important.
  • #1
charliemagne
12
0
A function is defined as a set of ordered-pairs where ...

But can we consider equations as functions?

Some says 'yes'.

Some says 'no', because according to them, equations are not actually functions. They are just used to define/represent functions.

example: y=4x+1/f(x)=4x+1.
Can we consider this as a function? Or, it is just an equation that defines/represents a function?

Thank you!
 
Physics news on Phys.org
  • #2


It really depends on the context. For most non set-theoretic purposes, saying the function f(x)=4x+1 is perfectly fine. Especially since the definition of a function as a set of ordered pairs is only developed for the use of studying functions in a set theoretic setting
 
  • #3


The people who respond "no" are being kind of ridiculous. I care very little for semantics when it contributes really nothing at all. Yes, of course f(x) = 4x + 1 is a function, or else why would we have gone through the trouble of creating the modern definition at all.
 

FAQ: Can we consider equations as functions?

What is the definition of an equation?

An equation is a mathematical statement that shows the relationship between two or more quantities. It typically includes variables, numbers, and mathematical operations.

How is an equation different from a function?

An equation is a mathematical statement, while a function is a rule that assigns each input value to a unique output value. An equation may or may not represent a function, depending on the values of the variables and the operations involved.

Can all equations be considered as functions?

No, not all equations can be considered as functions. For an equation to represent a function, each input value must correspond to exactly one output value. If there are multiple output values for a single input value, the equation does not represent a function.

How can we determine if an equation represents a function?

To determine if an equation represents a function, we can use the vertical line test. If a vertical line can be drawn through the graph of the equation and only touches the graph at one point, then the equation represents a function. If the vertical line intersects the graph at multiple points, then the equation does not represent a function.

Why is it important to consider equations as functions?

Considering equations as functions allows us to better understand the relationships between different quantities and make predictions about their behavior. It also allows us to use mathematical tools, such as graphs and tables, to analyze and solve problems related to the equation.

Similar threads

Is ##f(x)=2^{x}-1## considered an exponential function?
Replies
12
Views
2K
Determine which set is a function
Replies
3
Views
1K
Find the range of the function ##f(x) = \frac{e^{2x}-e^x+1} {e^{2x}+e^x+1}##
Replies
8
Views
1K
Range of a function involving trigonometric functions
Replies
11
Views
926
To find the range of a given ##\sin## function
Replies
15
Views
1K
How to graph by hand: y=log((x/(x+2))
Replies
3
Views
997
Solving a nested logarithmic equation
Replies
2
Views
1K
If ##x> 1## and ##x^2 <2##, prove ##x < y##, ##y^2<2##
Replies
10
Views
1K
Suppose the function f is defined as follows: f(x)=4x^2-5x+1
Replies
10
Views
4K
Curiosity about why this is not a Function composition
Replies
7
Views
3K

Hot Threads

Recent Insights

Back
Top