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Rhenane
6 months ago

First comes the name of the function (here f). The quantity of the definition range (here the range of the real numbers) which is mapped to the following quantity of the value range (here the quantity of real numbers) then comes behind the double point (here the quantity of real numbers) . Then the actual assignment follows: here, the value x2 is assigned to each x of the definition quantity. If you now draw “all” assignments to a coordinate system, you will receive the image of a parabola in this case.

Does it mean? not R->R but, for example, Z->R (i.e. Def. range the whole numbers), then the parabel consists only of points, namely at the points where x is integer; the spaces remain free.

Rhenane
6 months ago

Yes, exactly one element of the set of values is assigned to each element from the set of definitions, then the assignment is a “function”.

Do you mean with your second paragraph that all real numbers should be allowed in the definition set, but in the image set only natural, i.e. R->N? However, it must then be ensured in the assignment rule that values also result from the image quantity, otherwise there is no function. This would only be in relatively few cases, for example with constant functions: f: R->N f(x)=3. Thus, the function value 3 is assigned to each real number. Or you define a “return function” which assigns the rounded amount to each x value. But these are now “special spinneries” which probably go a bit too far.

Rhenane
6 months ago

On the left is the amount of definition, i.e. what can be considered as elements. What’s going to get out when you’re in, must be the right side.

This means that only integer values are suitable for x at f(x)=x2-0.5 with Def. quantity Z. The square numbers minus 0.5, i.e. x=1, f(1)=12-0.5=0.5, are then assigned out, so the function f contains the number pair (1|0.5).

LUKEars
6 months ago

the syntax is:

Name: Def-Menge --> Bild-Menge, f(x) = Formel

wenn D die Definitionsmenge ist und f die Funktion, dann hat f die Bildmenge B=f(D) und es gilt:
Für alle d in D gibt es ein b in b, so dass gilt f(d)=b.

alles klar?
LUKEars
6 months ago
Reply to  Flo162728281

I have added my answer accordingly…

at f(x)=x2 you can limit the image quantity to non-negative real numbers if the DefMenge is real… if the DefMenge is integer, then the BMenge is natural-numbered with zero…

LUKEars
6 months ago

you don’t have to give the image amount to a minimum… so if the function maps everything to 1, you can still take the amount of real numbers as a picture amount…

in the DefMenge it is different… f(x)=1/x is not defined for x=0… so in the case the 0 strictly does not belong to the DefMenge…

so… f:X –> IN

or?