Question

Which of these relations are functions?

Option 1: x 1 2 3 4, y 2 4 6 13
Option 2: (3,2), (-1,7), (-3,1), (0,9), (2, -4)
Option 3: x 2 3 4 5, y 8 12 16 20
Option 4: x -1 0 1 2, y 3 5 7 9

Answer 1

Upon reviewing each option, we find that they all fit the definition of a function because every x-value corresponds to a unique y-value. Therefore, Options 1, 2, 3, and 4 are all functions.

Step-by-step explanation:

To determine which of the given relations are functions, we must understand the definition of a function in mathematics. A function is a relation in which every input (x-value) has a unique output (y-value). This means that in a function, each x-coordinate is associated with exactly one y-coordinate.

Let's examine each option using this definition:

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• Option 1: x 1 2 3 4, y 2 4 6 13 - Each x-value is mapped to a unique y-value, so this is a function.
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• Option 2: (3,2), (-1,7), (-3,1), (0,9), (2, -4) - Each x-value is unique and corresponds to one y-value, which means this set of ordered pairs is a function.
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• Option 3: x 2 3 4 5, y 8 12 16 20 - Similar to the prior examples, each x-coordinate here has a distinct y-coordinate. Thus, this is a function.
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• Option 4: x -1 0 1 2, y 3 5 7 9 - As with the others, we have unique x-values with corresponding unique y-values, so this, too, is a function.

Based on the provided definitions, all options (1, 2, 3, and 4) are examples of functions due to the one-to-one relationship between x and y-values.