# What does it mean when a function is undefined?

• lonewolf219
In summary, the conversation discusses the concept of undefined functions and their relationship to points on a graph. It is clarified that a function can be undefined at a certain point, such as (0,0), without indicating that the function does not pass through that point. The function is defined for individual real numbers, not pairs of numbers. It is also mentioned that functions can be undefined at certain points but still defined for other points.
lonewolf219
If a function is undefined at (0,0), does that mean the function does not pass through the origin? in general, if the function is undefined at a certain point, is that because it does not pass through that specific point?

hi lonewolf219!
lonewolf219 said:
… in general, if the function is undefined at a certain point, is that because it does not pass through that specific point?

i don't know what you mean by "pass through"

functions don't move, they just are

the function is defined on the subspace consisting of the whole space except that point

y=x^2

The graph of this function doesn't "pass through" the point (20,0). Am I correct to say the function y=x^2 is undefined at the point (20, 0) because this point does not lay on the curve of the function? Or would you say the function does not exist at that point...

If I understood what you meant, a function is undefined if it is not continuous at that point (like a cusp, or a jump)?

hi lonewolf219!

(try using the X2 button just above the Reply box )
y=x^2

The graph of this function doesn't "pass through" the point (20,0). Am I correct to say the function y=x^2 is undefined at the point (20, 0) because this point does not lay on the curve of the function? Or would you say the function does not exist at that point. …

ah, i see what you mean

no, the function y = x2 isn't defined on ℝ2, it's only defined on ℝ

y is defined at all values of x, not of (x,y)

(eg y is defined at 0,and the graph goes through (0,0))
lonewolf219 said:
If a function is undefined at (0,0), does that mean the function does not pass through the origin? in general, if the function is undefined at a certain point, is that because it does not pass through that specific point?

if a function z is undefined at (0,0), that means the graph (a surface) has a hole in above the origin

You need to be careful about exactly what a function is. The function y= f(x) maps real numbers to real numbers. It is, or is not, defined for individual real numbers, not pairs of numbers. $f(x)= x^2$ is defined for all real numbers. The function $f(x)= 1/x^2$ is defined for all x except x= 0 where it is "undefined".

Similarly, $f(x,y)= 1/(x^2+ y^2)$ is a function that maps (x, y), a point in R2, to a real number. It is undefined for (0, 0) and defined for all other (x, y).

I hope I know what you guys know one day...

you guys are brilliant!

## 1. What exactly does it mean when a function is undefined?

When a function is undefined, it means that the function does not have a valid output for certain inputs. This could be due to a variety of reasons, such as dividing by zero, taking the square root of a negative number, or using a variable that has not been defined.

## 2. Can a function be partially undefined?

Yes, a function can be partially undefined. This means that while the function may have a valid output for some inputs, it may not have a valid output for others. This often occurs when there are restrictions on the domain of the function.

## 3. How do I know if a function is undefined?

If you are given a specific input for a function and you are unable to find a corresponding output, then the function is undefined for that input. Another way to determine if a function is undefined is by analyzing the algebraic expression of the function and looking for any potential restrictions on the domain.

## 4. What happens when a function is undefined?

When a function is undefined, it means that the function cannot be evaluated and therefore does not have a valid output. This could result in an error message or an indication that the function is undefined, depending on the context in which the function is being used.

## 5. Can an undefined function be defined?

Yes, an undefined function can be defined by assigning restrictions on the domain or by using a different mathematical expression. However, it is important to note that the new definition may not be consistent with the original intention of the function and could lead to different results.

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