How do you graph a function that has a domain of all real numbers?

Domain. The domain of a function is the complete set of possible values of the independent variable. In plain English, this definition means: The domain is the set of all possible x -values which will make the function "work", and will output real y -values. When finding the domain, rememberStep-by-step explanation:

Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x

x

-axis. The range is the set of possible output values, which are shown on the y

y

-axis. Keep in mind that if the graph continues beyond the portion of the graph we can see, the domain and range may be greater than the visible values.

Graph of a polynomial that shows the x-axis is the domain and the y-axis is the range

We can observe that the graph extends horizontally from −5

−5

to the right without bound, so the domain is [−5,∞)

[−5,∞)

. The vertical extent of the graph is all range values 5

5

and below, so the range is (−∞,5]

(−∞,5]

. Note that the domain and range are always written from smaller to larger values, or from left to right for domain, and from the bottom of the graph to the top of the graph for range.

Example: Finding Domain and Range from a Graph

Find the domain and range of the function f

f

.

Graph of a function from (-3, 1].

Show Solution

This graph has three lines, two straight and one that is curvy. It shows that the domain starts at -3 (not including -3) all the way to 1. The range shows from -4 to 0.

Example: Finding Domain and Range from a Graph of Oil Production

Find the domain and range of the function f

f

.

Graph of the Alaska Crude Oil Production where the y-axis is thousand barrels per day and the -axis is the years.