A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one.
To Find: Function is one to one.
given function is not one to one.
You can determine whether or not the given function is one to one by just looking at the graph with the help of Horizontal Line Test. Horizontal Line Test says that a function is one to one if and only if any horizontal line intersects the graph of given function exactly at one point. In other words, the Horizontal Line Test can be stated as:
A function is NOT one to one if and only if there exists a horizontal line which intersects the graph of given function at least at two points.
Conclusion: Any horizontal line will intersect the given graph exactly once. Therefore, by using the Horizontal Line test, we can conclude that the given function is one to one.
Note: If you have to say that the given function is not one to one by Horizontal Line test, then existence of just one horizontal line, which intersects the given graph more than once, is sufficient.