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Which graph shows a set of ordered pairs that represent a function?

On a coordinate plane, solid circles appear at the following points: (negative 2, 3), (negative 1, 2), (1, 1), (2, negative 1), (2, negative 3), (4, negative 5).

On a coordinate plane, solid circles appear at the following points: (negative 4, negative 4), (negative 2, 2), (1, 1), (2, negative 5), (4, negative 3), (4, 4).

On a coordinate plane, solid circles appear at the following points: (negative 3, 2), (negative 2, 2), (0, 1), (1, 3), (2, negative 4), (4, negative 1).

On a coordinate plane, solid circles appear at the following points: (negative 4, 2), (negative 2, 1), (negative 2, negative 1), (0, negative 2), (0, negative 4), (2, negative 5).

Respuesta :

A function must associate only one output to each input. So, you must rule out all the ordered pairs that associate two outputs to the same input.

In the first answer we have both [tex](2,-1)[/tex] and [tex](2,-3)[/tex]. So, this is not a function because there is ambiguity defining [tex]f(2)[/tex]. Should it be [tex]f(2)=-1[/tex] or [tex]f(2)=-3[/tex]?

In the second answer we have both [tex](4,-3)[/tex] and [tex](4,-4)[/tex]. So, this is not a function because there is ambiguity defining [tex]f(4)[/tex]. Should it be [tex]f(4)=-3[/tex] or [tex]f(4)=-4[/tex]?

The third answer is a function because all input-output associations are unique: we have

[tex]f(-3)=2,\ \ f(-2)=2,\ \ f(0)=1,\ \ f(1)=3,\ \ f(2)=-4,\ \ f(4)=-1[/tex]

In the fourth answer we have both [tex](-2,1)[/tex] and [tex](-2,-1)[/tex]. So, this is not a function because there is ambiguity defining [tex]f(-2)[/tex]. Should it be [tex]f(-2)=1[/tex] or [tex]f(-2)=-1[/tex]?

The set of ordered pairs that represent a function (- 3, 2), (- 2, 2), (0, 1), (1, 3), (2, -4), (4, -1). Then the correct option is C.

What is a function?

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

For the function, for each value of the independent variable, the value of dependent variable should be different.

For each value of the variable x, the value of the variable y should be different.

Let check all the options:

A. On a coordinate plane, solid circles appear at the following points:

(- 2, 3), (- 1, 2), (1, 1), (2, -1), (2, -3), (4, -5).

At x = 2, the values of y are -1, and -3.

B. On a coordinate plane, solid circles appear at the following points:

(- 4, -4), (- 2, 2), (1, 1), (2, -5), (4, -3), (4, 4).

At x = 4, the values of y are -4, and -3.

C. On a coordinate plane, solid circles appear at the following points:

(- 3, 2), (- 2, 2), (0, 1), (1, 3), (2, -4), (4, -1).

For each value of x, the value of y is different.

D. On a coordinate plane, solid circles appear at the following points:

(- 4, 2), (- 2, 1), (- 2, -1), (0, -2), (0, -4), (2, -5).

At x = -2, the values of y are -1, and 1.

At x = 0, the values of y are -2, and -4.

Then the correct option is C.

More about the function link is given below.

https://brainly.com/question/5245372

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