Which of the following best describes the graph below? A. It is a one-to-one function. B. It is not a function. C. It is a function, but it is not one-to-one. D. It is a many-to-one function.

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Question:

Which of the following best describes the graph below? A. It is a one-to-one function. B. It is not a function. C. It is a function, but it is not one-to-one. D. It is a many-to-one function.

We want to analyze the given graph.

We can see that this is a one-to-one function, so the correct option is A.

We define a function as a relationship that maps elements from one set into elements of other set, such that each element of the first set can be mapped into only one element of the second set.

We define a one-to-one function as a function where every element on the second set is being mapped from only one element in the first set.

To see if a function is one-to-one, we can draw a horizontal line in any part of the graph.

If it touches the graph more than once, then the function is not one-to-one.

Here we can perform that test and we will see that the horizontal line never touches the graph twice, thus this is a one-to-one function, and the correct option is A.

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