Question

the road mileage between city m and several selected cities is shown in the table. if we consider this as a function that pairs each city with a distance, is the function a one-to-one function?

city	distance to city m (in miles)
city b	758
city c	1114
city d	607
city e	1114
city f	1286

is the function a one-to-one function?
○ yes
○ no

Explanation:

Step1: Recall one - to - one function definition

A one - to - one function is a function where each element in the range (output) corresponds to exactly one element in the domain (input). In other words, if \(f(x_1)=f(x_2)\), then \(x_1 = x_2\) for all \(x_1,x_2\) in the domain.

Step2: Analyze the given function

The domain of the function is the set of cities \(\{City\ A, City\ B, City\ C, City\ D, City\ E, City\ F\}\) and the range is the set of distances \(\{1411, 758, 1114, 607, 1114, 1286\}\). We can see that the distance \(1114\) miles is paired with two different cities: City C and City E. That is, \(f(City\ C)=1114\) and \(f(City\ E) = 1114\), but \(City\ C
eq City\ E\). So the function does not satisfy the definition of a one - to - one function.

Answer:

No