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Which of the following rules represents a function

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RASTA

RASTA aktiv_icon

17:14 Uhr, 08.01.2022

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Tag,
Which of the following rules represents a function?
Welche der folgenden Regeln stellt eine Funktion dar?

can you explain why these are called rules?.
i know about functions but confused here about they call these rules?
please, any hinto with the subject/topic at hand. can you refer a tutorial or begin a solution. however way you think it is best, now you know i am here to get you to do my homework but to explain the way I should go and the materials available. you can refer german sites too. i dont speak much but can read German.

Danke im Voraus.

Which of the following rules represents a function?

Choose an answer
{(x,y):y2=x2}
{(x,y):y=x2}
{(x,y):|y|=x2}
{(x,y):y2=x}
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supporter

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17:38 Uhr, 08.01.2022

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123mathe.de/relationen-und-funktionen
RASTA

RASTA aktiv_icon

18:04 Uhr, 08.01.2022

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thank you. Ich melde mich noch!.
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Roman-22

Roman-22

18:47 Uhr, 08.01.2022

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A "function rule" simply is an equation which defines a function - it describes a functional relationship.
y=x2+1 is an example for a function rule.
y4=x is a rule, but its not a function rule, because a function has to be unique (every x is assigned just one y). Here for x=1 we have two possible values for y, either +1 or -1. So this rules defines a relation which is not unique and therefore is not a function.

Now check your given rules if they define a function (unique relation) or not.
RASTA

RASTA aktiv_icon

21:07 Uhr, 08.01.2022

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I do not understand well,
can you provide an example?.
Graphing the equations given in Desmos I could see that b) is the right choice becasue it passes the vertical test,
but, they won't let me do it with the graph,
how can i do it assigning values to what variable, x or y?
don't really understand your explanation. thanks!

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Roman-22

Roman-22

22:35 Uhr, 08.01.2022

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> can you provide an example?.
I did. It was y4=x.

And, yes, only b) is a function and what you describe with "vertical test" is exactly what I meant when I wrote that the relation has to be unique to be called a function. At every x position there must be no more than just one assigned y value.

To "see" if the relation is unique without plotting the relation, you would do the plotting in your mind. If you find just one x-value with two or more assigned y-values, than its not a function.

For example |y|=x2. You know that e.g. both |+4| and |-4| simplify to +4. This means that for x=2(x2=4) there are two possible values for y(+4 and -4) and this contradicts the characterizing property of a function.
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RASTA

RASTA aktiv_icon

20:22 Uhr, 09.01.2022

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I got clearly!

I gave a value to x,
- if I get 2 values of y for the same x then it is not a function.

So for the equation A>x2=y2.
For x=1, you can get y=-1 or 1. So it is not a function.

Equation B gave me only one value so it's a function.

Because there is one y-value for the entered x-value, and only one.

x=2, then, y=4 when x=2
y=x2
y=4

Vielen Danke.