Final answer:
A set of ordered pairs does not represent a function if an x-value is paired with multiple y-values. In the options provided, Option 1 and Option 3 both contain the x-value of 1 with different y-values, thus not representing a function when considered together.
Step-by-step explanation:
The ordered pairs given are: Option 1: (1, 1.5), Option 2: (2, 3), Option 3: (1, 4), and Option 4: (0, 1). To determine which set of ordered pairs does not represent a function of x, we need to look for any instances where a single x-value is paired with multiple y-values. Considering the definition of a function, every x-value in the domain should map to exactly one y-value in the range.
Upon examination, Option 1 and Option 3 both contain the x-value of 1; however, they are paired with different y-values (1.5 and 4, respectively). This violates the definition of a function, where each input (x-value) must be associated with only one output (y-value). Therefore, combining Option 1 and Option 3 into a set does not represent a function as it stands.
Option 2 and Option 4 each have distinct x-values, therefore, they represent functions by themselves. To correctly identify a non-function, one should look for repeated x-values with different corresponding y-values within a single set of ordered pairs.