Question

The road mileage between Denver, Colorado, and several selected U.S. cities is shown in the table. If we consider this as a function that pairs each city with a distance, is it a one-to-one function? How could we change the answer to this question by adding 1 mile to one of the distances shown?

Name: Problem 3, Chapter 12: Beginning and Intermediate Algebra
Uploaded: 2020-07-13T23:30:59-08:00
Duration: 2 min 28 s
Channel: Melissa Salvador
Description: The road mileage between Denver, Colorado, and several selected U.S. cities is shown in the table. If we consider this as a function that pairs each city with a distance, is it a one-to-one function? How could we change the answer to this question by adding 1 mile to one of the distances shown?

   The road mileage between Denver, Colorado, and several selected U.S. cities is shown in the table. If we consider this as a function that pairs each city with a distance, is it a one-to-one function? How could we change the answer to this question by adding 1 mile to one of the distances shown?

Beginning and Intermediate Algebra

Margaret L. Lial ,… 5th Edition

Chapter 12, Problem 3

Instant Answer

Solved by Expert Melissa Salvador

07/13/2020

Step 1

A function is said to be one-to-one (or injective), if the function assigns a unique output to each unique input. In other words, no two different inputs will produce the same output. Show more…

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The road mileage between Denver, Colorado, and several selected U.S. cities is shown in the table. If we consider this as a function that pairs each city with a distance, is it a one-to-one function? How could we change the answer to this question by adding 1 mile to one of the distances shown?

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Key Concepts

One-to-One Function (Injective Function)

An injective or one-to-one function is one in which every distinct input maps to a distinct output. This means no two different cities would have the same road mileage value, ensuring each output is unique.

Function Modification and Its Impact on Injectivity

Changing the function by adding 1 mile to one of the distances can affect its injectivity. If the new distance becomes equal to a distance already assigned to another city, the function would no longer be one-to-one, highlighting how minor adjustments can impact the uniqueness of pairings in a function.

Function

A function is a rule that assigns each element from one set (the domain) a unique element in another set (the range). In this problem, the cities are the elements in the domain, and each is paired with a road mileage value in the range.

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