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Which of the following rules represents a function

Schüler

Tags: Mathematik

RASTA aktiv_icon

17:14 Uhr, 08.01.2022

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) : y 2 = x 2}

{(x, y) : y = x 2}

{(x, y) : | y | = x 2}

{(x, y) : y 2 = x}

supporter aktiv_icon

17:38 Uhr, 08.01.2022

123mathe.de/relationen-und-funktionen

RASTA aktiv_icon

18:04 Uhr, 08.01.2022

thank you. Ich melde mich noch!.

Roman-22

18:47 Uhr, 08.01.2022

A "function rule" simply is an equation which defines a function - it describes a functional relationship.

y = x^{2} + 1

is an example for a function rule.

y^{4} = 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

- 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 aktiv_icon

21:07 Uhr, 08.01.2022

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!

Roman-22

22:35 Uhr, 08.01.2022

>

can you provide an example?.
I did. It was

y^{4} = 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 | = x^{2}

. You know that

e . g

. both

| + 4 |

and

| - 4 |

simplify to

+ 4

. This means that for

x = 2 (\to x^{2} = 4)

there are two possible values for

y (\to + 4

and

- 4)

and this contradicts the characterizing property of a function.

RASTA aktiv_icon

20:22 Uhr, 09.01.2022

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 > x^{2} = y^{2}

.
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 = x^{2}

y = 4

Vielen Danke.

1549006

1548922

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