DETERMINE WHETHER THE RELATION REPRESENTS A FUNCTION

Which of the following sets of ordered pairs are functions ? Give reasons for your answers.

1)  (1, 1), (2, 2), (3, 3), (4, 4)

2)  (-1, 2), (-3, 2), (3, 2), (1, 2)

3)  (2, 5), (-1, 4), (-3, 7), (2, -3)

4)  (3, -2), (3, 0), (3, 2), (3, 4)

5)  (-7, 0), (-5, 0), (-3, 0), (-1, 0)

6)  (0, 5), (0, 1), (2, 1), (2, -5)

Problem 1 :

(1, 1), (2, 2), (3, 3), (4, 4)

Solution :

Let X be the set of inputs and Y be the set of outputs.

Inputs (x)  =  {1, 2, 3, 4}

Outputs (y)  =  {1, 2, 3, 4}

Create a mapping of the following relation,

Form the arrow diagram, we understand that each x-value is being paired with only one y-value.

Or simply each input has at most one output. So, it is a function.

Problem 2 :

(-1, 2), (-3, 2), (3, 2), (1, 2)

Solution :

Let X be the set of inputs and Y be the set of outputs.

Inputs (x)  =  {-1, -3, 3, 1}

Output (y)  =  {2}

Create a mapping of the following relation,

Because input has atmost only one output. So, it is a function.

Problem 3 :

(2, 5), (-1, 4), (-3, 7), (2, -3)

Solution :

Let X be the set of inputs and Y be the set of outputs.

Inputs (X)  =  {2, -1, -3, 2}

Output (Y)  =  {5, 4, 7, -3}

Create a mapping of the following relation,

By observing the arrow diagram, one of the input has more than one output. So, it is not a function.

Problem 4 :

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

Solution :

Let X be the set of inputs and Y be the set of outputs.

Inputs (x)  =  {3}

Outputs (S)  =  {-2, 0, 2, 4}

Create a mapping of the following relation,

The input 3 has associate with more than one output. So, it is not a function.

Problem 5 :

(-7, 0), (-5, 0), (-3, 0), (-1, 0)

Solution :

Let X be the set of inputs and Y be the set of outputs.

The set of x  =  {-7, -5, -3, -1}

The set of y  =  {0}

Create a mapping of the following relation,

Each input is associated with only one output, but no input is having more than one output. So it is a function.

Problem 6 :

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

Solution :

Let X be the set of inputs and Y be the set of outputs.

Inputs(x)  =  {0, 2}

Outputs (Y)  =  {5, 1, -5}

Create a mapping of the following relation,

Since the inputs 0 and 2 are having more than one output, it is not a function.

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