Which of the following represents a function?

Functions cannot have different values of y for the same value of x. Now let us check each case one at a time.

First Case: For the same value of x=-1, y has two different values of 7 and 1, which is not allowed in a function. Therefore, the first case is not a function.

Second Case: For the same value of x=-1, y has two different values of -5 and 1, which is not allowed in a function. Therefore, the second case is not a function.

Third Case: For the same value of x=3, y has two different values of 2 and 4, which is not allowed in a function. Therefore, third case is not a function.

Fourth Case: In this case no value of x is same. So, this is a function.

A relation can be regarded as a function if the x values are unique for every y-value.

The relation (option d) represents a function

(a) The table

The table has the same x-values for y values of 7 and 1.

i.e

Hence, the table is not a function

(b) The graph

The graph has the same x-values for y values of -5 and 1.

i.e

Hence, the graph is not a function

(c) The ordered pair

The ordered pair has the same x-values for y values of 2 and 4.

i.e

Hence, the ordered pair is not a function

(d) The relation

For every y-value, there is a corresponding and unique x-value.

Hence, the relation is a function

Read more about functions and relations at:

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