How do you know if a graph is one-to-one?
A one-to-one function is a function in which for each value of the domain, there is a unique output/range in the graph of the function.
Answer: Any function that follows the horizontal line test, can only be classified as a one-to-one function.
Let's go through the explanation to understand better.
Explanation:
The one-to-one function is also called the injective function. It is the function wherein all the values from one set map to a unique value in the codomain set.
Here is a test to find out if a graph is one-to-one or not.
A horizontal line test is used to verify if the function is one-to-one or not. This test states that if a horizontal line drawn to the graph intersects the graph more than one time then the function cannot be one-to-one.
Only if the horizontal line intersects the graph once, then it can be termed as a one-to-one function.
The cosine function is not a one-to-one function, while the second function follows the horizontal line test, and is thus a one-to-one function.