A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one. f(t) is your height at age t.
To Find: Function is one to one.
given function is not one to one.
When our age increases, so does our height. But after a certain point in our growth, age increases, but height remains constant. The graph for this function will look like:
After age 20, height remains constant.
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) 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.