A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one. g(x)=1sinx
To Find: Function is one to one.
given function is not one to one.
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 point.
Conclusion: Since any horizontal line (except at the point of minima and maxima) will intersect the given graph more than once, by using the Horizontal Line Test, we can conclude that the given function is not one to one.
For example, take two points 0 and . Then,, for two distinct values, their images are the same. Therefore, the given function is not 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.