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Determining the Range from a Set of Ordered Pairs

The set of ordered pairs [tex]\((-1, 8), (0, 3), (1, -2), (2, -7)\)[/tex] represents a function. What is the range of the function?

A. [tex]\(\{x: x=-1, 0, 1, 2\}\)[/tex]
B. [tex]\(\{y: y=-7, -2, 3, 8\}\)[/tex]
C. [tex]\(\{x: x=-7, -2, -1, 0, 1, 2, 3, 8\}\)[/tex]
D. [tex]\(\{y: y=-7, -2, -1, 0, 1, 2, 3, 8\}\)[/tex]



Answer :

GinnyAnswer
First, let's understand the concept of a function and its range. The range of a function consists of all the possible output values (y-values) that the function can produce.

We are given the following ordered pairs: [tex]\((-1, 8)\)[/tex], [tex]\((0, 3)\)[/tex], [tex]\((1, -2)\)[/tex], and [tex]\((2, -7)\)[/tex]. Each of these ordered pairs consists of an x-value (input) and a corresponding y-value (output).

To find the range, we need to extract all the y-values from these pairs:
- The y-value from [tex]\((-1, 8)\)[/tex] is 8.
- The y-value from [tex]\((0, 3)\)[/tex] is 3.
- The y-value from [tex]\((1, -2)\)[/tex] is -2.
- The y-value from [tex]\((2, -7)\)[/tex] is -7.

Now, list these y-values: 8, 3, -2, -7.

Next, we should identify the distinct y-values and sort them in ascending order:
- The distinct y-values are: 8, 3, -2, -7.
- Sorting them in ascending order results in: -7, -2, 3, 8.

Therefore, the range of the function is: [tex]\(\{-7, -2, 3, 8\}\)[/tex].

This matches the answer choice:
[tex]\(\{y: y = -7, -2, 3, 8\}\)[/tex].

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