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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steve should create a type of business report called a business plan. the correct option among the options that are already given in the question is the last or the fourth option. this business report created by steve will actually influence the investors about investing their money in steve's business. this business report will have all the details about the business, the amount of investment required and the amount of expected profit.

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