# How do you know if a graph is one-to-one?

A one-to-one function is that function in which for each value of a domain, there is a unique 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 on the other set.

Look at the properties of a one-to-one function.

If f and g are both one-to-one then fog is also a one-to-one function.

If both A and B are limited with the same number of elements, then f: A → B is one-one, if and only if f is surjective or onto function.

If f: A → B is one-one and P and Q are both subsets of A, then f(P ∩ Q) = f(P) ∩ f(Q).

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 mapped as 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.