Question

Which of the following sets of ordered pairs (x,y) is NOT a function of X?

a) {(0,0), (1, 1), (2, 1)}
b) {(0,1), (1, 1), (2, 1)}
c) {(0,0), (1, 1), (2, 2)}
d) {(0,1), (1,0), (1, 1)}

Answer 1

A function must have only one output for each input. Upon examining the given sets of ordered pairs, it is found that set d) {(0,1), (1,0), (1, 1)} has the input x = 1 paired with two different outputs, which means it does not represent a function of x.

Step-by-step explanation:

A function is a relation in which every input (usually represented by the variable x) is associated with exactly one output (usually represented by the variable y). When looking at a set of ordered pairs to determine if it represents a function, each x-value should be paired with only one y-value. If an x-value is paired with more than one y-value, then the set of ordered pairs does not represent a function of x.

Let's examine the given sets of ordered pairs:

• a) {(0,0), (1, 1), (2, 1)} - Every x-value is associated with one y-value.
• b) {(0,1), (1, 1), (2, 1)} - Every x-value is associated with one y-value.
• c) {(0,0), (1, 1), (2, 2)} - Every x-value is associated with one y-value.
• d) {(0,1), (1,0), (1, 1)} - Here, the x-value 1 is associated with two different y-values (0 and 1), which violates the definition of a function.

Therefore, the set of ordered pairs that is not a function of x is option d.