Question

Which of the following sets of ordered pairs do not belong

Answer 1

First and last options do not belong to a one-to-one function

Explanation:

Definition of a one-to-one function

A function f is 1 -to- 1 if no two elements in the domain of f correspond to the same element in the range of f .

In other words, for each x value there is only one y value

And, no y value corresponds to more than one x

In the given problem we test the set of ordered pairs to see if a y-value corresponds to more than one x-value. If so, the ordered pair does not belong to a one-to-one function

1. In the first option we see that the value of x = 1 maps to two y values : -4 and -2. By the definition of a function, a single x value cannot result in two different y values. So this set does not even belong to a function let alone a 1:1 function
2. The second option - set belongs to a 1:1 function since for any value of x there is only one value of y
3. The third option is a 1:1 function
4. The last option does have unique y values for x values so it is a function but for x = 2 and x = 5 we get the same y= -1 so it is not a 1:1 function