What makes function different from relation

What a mess! The relation "height indicates name" is not well-behaved. It is not a function. For a relation to be a function, there must be only and exactly one y that corresponds to a given x.

Here are some pictures of this:. Now YOU try! The "Vertical Line Test". This characteristic of non-functions was noticed by I-don't-know-who, and was codified in "The Vertical Line Test": Given the graph of a relation, if you can draw a vertical line that crosses the graph in more than one place, then the relation is not a function.

Here are a couple examples:. Think of all the graphing that you've done so far. In other words, if you can enter it into your graphing calculator, then it's a function. The calculator can only handle functions. Do you take the positive square root, or the negative? So, in this case, the relation is not a function.

You can also check this by using our first definition from above. Stapel, Elizabeth. Accessed [Date] [Month] This is a function. In f x , any input that is less than the value a must be plugged into g. On the other hand, if your input is greater than or equal to a , h x gives you the correct output for f. Remember that the inequality restrictions are based on the number you input , not the output of the function.

You now know enough to determine whether given relations possess the proper characteristics to be classified as functions. Example 3: Explain why, in each of the following relations, y is not a function of x. Because one input cannot have two corresponding outputs, this is not a function. Previous Inverse Functions. Next Polynomial and Rational Functions. Removing book from your Reading List will also remove any bookmarked pages associated with this title. Are you sure you want to remove bookConfirmation and any corresponding bookmarks?

My Preferences My Reading List. A relation is a collection of ordered pairs, which contains an object from one set to the other set.

Consider two arbitrary sets X and Y. The product is designated as, read as X cross Y. The Cartesian product deals with ordered pairs, so the order in which the sets are considered is important. Using n A for the number of elements in a set A, we have:. A relation X to Y is a subset of X Y. Let X and Y set. An ordered pair x,y is called a relation in x and y. The first element in an ordered pair is called the domain, and the set of second elements is called the range of the relation. So all functions are relations while all relations are not functions.

Let's compare relations and functions. Explanation: By the definition, relations and functions seem to be quite similar but actually, there is a major difference between them. Thus, we have seen the differences between relations and functions. Explore math program.