Professor Jordan

Domain and Range

The domain and range of a function are all of the values of a function. The Domain of a function is the group of all of the possible values for x, or all of the possible input values. The Range of a function is the group of all of the possible values for x, or the output values. The domain and range can have both negative and positive numbers.

Ex. (-3, 3) (5, 2) (10, -1)

          X   Y   X   Y     X     Y

Domain: -3. 5. 10

Range: -1. 2, 3

When stating the domain and range, the numbers have to go in order from least to greatest.

Ex. 2 (-3. 3) (-3, 5) (1, 7) (3, 9)

Domain: -3, 1, 3

Range: 3, 5, 7, 9

NOTE: The domain in this example repeats values. In this instance, this set of values does NOT make a function because X values cannot repeat. They do not pass the Vertical Line Test, which is a method of determining whether or not a graph is a function.

Y values, however, can repeat:

Ex. 3 (-3, 18) (10, 18) (15, 18)

Domain: -3, 10, 15

Range: 18

You can also determine the domain and range from a graph:

Ex. 4

(0,1) (1,2) (2,3) (3,4) (4, 5) (5, 6)

Domain: 0, 1, 2, 3, 4, 5,

Range: 1, 2, 3, 4, 5, 6

Ex. 5

Domain: All Real numbers

Range Y  ≥ 2

This is all Real numbers, or ℝ because X has every and any possible value for X. it can be any real number (any positive or negative whole number). The Range is Y is GREATER THAN OR EQUAL TO 2. This is because the graph has the lowest point at 2, and the graph goes up higher. That means that the graph's range is equal to 2 and any number higher than 2