What makes a set of ordered pairs a function

Note: f 3 is not f times 3. A function is a special type of relation. A relation is just a set of ordered pairs x , y. In formal mathematical language, a function is a relation for which:. This just says that in a function, you can't have two ordered pairs with the same x -value but different y -values. If you have the graph of a relation, you can use the vertical line test to find out whether the relation is a function. Names of standardized tests are owned by the trademark holders and are not affiliated with Varsity Tutors LLC.

The numbers are written within a set of parentheses and separated by a comma. For example, 4, 7 is an ordered-pair number; the order is designated by the first element 4 and the second element 7.

The pair 7, 4 is not the same as 4, 7 because of the different ordering. Sets of ordered-pair numbers can represent relations or functions. The following diagram shows some examples of relations and functions. Scroll down the page for more examples and solutions on how to determine if a relation is a function. The pairing of the student number and his corresponding weight is a relation and can be written as a set of ordered-pair numbers.

The set of all first elements is called the domain of the relation. The set of second elements is called the range of the relation. By looking at the denominator of , there will be a discontinuity. Since the denominator cannot be zero, set the denominator not equal to zero and solve the value of. There is a discontinuity at.

To determine what type of discontinuity , check if there is a common factor in the numerator and denominator of. While real numbers correspond to points on a line, ordered pairs of real numbers correspond to points on a plane. An ordered pair of real numbers , a, b , is given by the first number a and the second number b. For example, 1, 3 , 3, 1 , and 1, 1 are three different ordered pairs. For this type of function, the domain is all real numbers.

A function with a fraction with a variable in the denominator. To find the domain of this type of function, set the bottom equal to zero and exclude the x value you find when you solve the equation. A function with a variable inside a radical sign. In mathematics, a function is a relation between sets that associates to every element of a first set exactly one element of the second set. The symbol that is used for representing the input is the variable of the function one often says that f is a function of the variable x.

The ordered pair -7, 1 is found in the coordinate system when you move 7 steps to the left on the x-axis and 1 step upwards on the y-axis. To find out the coordinates of a point in the coordinate system you do the opposite. Begin at the point and follow a vertical line either up or down to the x-axis. A relation is a relationship between sets of values. In math , the relation is between the x-values and y-values of ordered pairs.

The set of all x-values is called the domain, and the set of all y-values is called the range.