http://www.ck12.org Chapter 1. Functions and Graphs
Solution:
Domain:x∈[− 3 ,− 1 )∪[ 0 , 3 )
Range:y∈[− 2 ,∞)
Note that the function seems to approach the vertical linex=−1 without actually reaching it. Also note the empty
hole at the point (3, 1) which is why the domain excludes thexvalue of 3.
Concept Problem Revisited
The three functions that have limited domains are the square root function, the log function and the reciprocal
function. The square root function has a restricted domain because you cannot take square roots of negative numbers
and produce real numbers. The log function is restricted because the log function is not defined to operate on non-
positive numbers. The reciprocal function is restricted because numbers that are divided by zero are not defined.
Vocabulary
Domainis the possiblexvalues or inputs of a function.
Rangeis the possibleyvalues or outputs of a function.
Interval notationis a tool for describing groups of numbers in the domain and range. Intervals are either open or
closed or both.
Open intervalsuse parentheses, (), and refer to intervals that do not include the end points. They are always used
with infinity.
Closed intervalsuse brackets, [], and refer to intervals that do include the end points.
Curly brackets,{}, are used when the domain or range are distinct numbers and not an interval of values.
∈is a symbol that stands for “is an element of”and tells you what kind of values an interval describes.
∪is a symbol that stands forUnionand is used to connect two groups together. It is associated with the logical term
OR.