Question

which of the following lists of ordered pairs is a function? a.(0,2),(4,2),(0,-4),(4,-2) b.(2,4),(3,9),(4,16),(5,25) c.(2,4),(-2,4),(3,9),(-2,-4) d.(1,1),(2,3),(1,5),(4,7)

Answer 1

A function will not have repeating x values....all the x values have to be different. They can have repeating y values, just not the x ones.
So which list of ordered pairs has all different x values ?
The answer would be : B...because ur x values are (2,3,4,5)...all different values.

Answer 2

Consider the given ordered pairs. We have to identify the function.

"A function is a relation and it is the set of ordered pairs that does not contain two pairs with the same first component".

Consider the first ordered pair,

A. (0,2),(4,2),(0,-4),(4,-2)

Since, these ordered pairs has '0' as the same first component in (0,2) and (0,-4). So, it is not a function.

Consider the second ordered pair,

B. (2,4),(3,9),(4,16),(5,25)

Since, these ordered pairs has all the different first component. So, this is a function.

Consider the third ordered pair,

C. (2,4),(-2,4),(3,9),(-2,-4)

Since, these ordered pairs has '-2' as the same first component in (-2,4) and (-2,-4). So, it is not a function.

Consider the fourth ordered pair,

D. (1,1),(2,3),(1,5),(4,7)

Since, these ordered pairs has '1' as the same first component in (1,1) and (1,5). So, it is not a function.

Therefore, the ordered pairs given in option B is a function.

So, Option B is the correct answer.