Question

The average mpg usage for a 2017 Toyota Prius for a sample of 21 tanks of gas was 45.4 with a standard deviation of 2.3. For a 2017 Ford Fusion, the average mpg usage for a sample of 21 tanks of gas was 43.8 with a standard deviation of 2.1. Which of the following relations is a function? A) (1, 4), (-2, 2), (8, 1), (-8, 2) B) (1, 4), (-2, 6), (1, 3), (-8, 2) C) (8, 1), (-2, 4), (1, 1), (8, 2) D) (1, 0), (-2, 3), (8, 1), (-2, 5)

Answer 1

The relation described in Option A is a function because each element of the domain is paired with exactly one element of the codomain, with no first element repeated with a different second element.

Step-by-step explanation:

The question given relates to mathematics and more specifically to functions. A function is a relation in which each element of the domain (the first value of the ordered pairs) is paired with exactly one element of the codomain (the second value of the ordered pairs). When determining whether a relation is a function, you will look for pairs with the same first element but different second elements.

Options Analysis

• Option A: (1, 4), (-2, 2), (8, 1), (-8, 2) - This is a function because all first elements are unique.
• Option B: (1, 4), (-2, 6), (1, 3), (-8, 2) - This is not a function because the first element '1' repeats with different second elements (4 and 3).
• Option C: (8, 1), (-2, 4), (1, 1), (8, 2) - This is not a function because the first element '8' repeats with different second elements (1 and 2).
• Option D: (1, 0), (-2, 3), (8, 1), (-2, 5) - This is not a function because the first element '-2' repeats with different second elements (3 and 5).

Based on this analysis, Option A represents a function because it does not contain any repeated first elements with different second elements.