Question

Which of the following sets of ordered pairs represents a function?

A.
{(-8,-14), (-7,-12), (-6,-10), (-5,-8)}
B.
{(-4,-14), (-9,-12), (-6,-10), (-9,-8)}
C.
{(8,-2), (9,-1), (10,2), (8,-10)}
D.
{(-8,-6), (-5,-3), (-2,0), (-2,3)}

Answer 1

A.

{(-8,-14), (-7,-12), (-6,-10), (-5,-8)}

Explanation:

In mathematics, a function
`f` is a relationship between a given set
`x` (domain) and another set of elements
`y=f(x)` (range) so that each element x in the domain corresponds to a single element
`f(x)` of the range. This can be expressed as:

`f:x \rightarrow y\\\\a \rightarrow f(a)\\\\Where\hspace{3}a\hspace{3}is\hspace{3}an\hspace{3}arbitrary\hspace{3}constant`

So according to that, the only set that satisfies the definition of a function is:

A.

{(-8,-14), (-7,-12), (-6,-10), (-5,-8)}

This is because:

In B.

-9 is the first element in more than one ordered pair in this set.

In C.

8 is the first element in more than one ordered pair in this set.

In D.

-2 is the first element in more than one ordered pair in this set.

Answer 2

A. {(-8,-14), (-7,-12), (-6,-10), (-5,-8)}

Explanation:

A function has no repeated values of the independent variable. Only choice A meets that requirement.

___

B: (-9, 12) and (-9, 8) both have -9 as a first value; not a function.

C: (8, -2) and (8, -10) both have 8 as a first value; not a function.

D: (-2, 0) and (-2, 3) both have -2 as a first value; not a function.