We can determine graphically if a given function is a one to one by drawing horizontal lines. Graph of a function that is not a one to one The graph in figure 4 below is that of a NOT one to one function since for at least two different values of the input x (x 1 and x 2 ) the outputs f(x 1 ) and f(x 2 ) are equal.įigure 4. The graph in figure 3 below is that of a one to one function since for any two different values of the input x (x 1 and x 2 ) the outputs f(x 1 ) and f(x 2 ) are different. If the graph of a function is known, it is fairly easy to determine if that function is a one to one or not using the horizontal line test. Venn diagram of a function that is not a one to one In the Venn diagram below, function f is NOT a one to one since the inputs -1 and 0 have the same output.įigure 2. In the Venn diagram below, function f is a one to one since not two inputs have a common output.įigure 1. This last property is useful in proving that a function is or is not a one to one.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |