1.4. Domain and Range http://www.ck12.org
b.(−∞, 0 )
c.[ 0 ,∞)
d. [1, 4]
e. (5, 6)
f. [ 1 , 2 )∪[ 10 , 25 ]Note: The∪symbol means Union and refers to the fact that if some numberxis in this union, then it is either in
the first group or it is in the second group. This symbol is associated with the OR statement. While it is true that
the Union symbol seems to bring one group and another group together, the symbol for AND is∩which means
intersection. Intersection is different from union because intersection means all numbers that are in both the first
group and second group at the same time.
Example B
Identify the domain and range for the following function.
Solution:
Domain:x∈[− 3 , 2 ]
Range:y∈[− 2 , 3 ]
Note that the∈symbol means “is an element of” and means that thexor theyis in that interval. Also note that the
numbers in the interval are always written in increasing order. [3, -2] is considered improper.
Lastly, note that even though the [-3, 2] may look similar to the ordered pair that represents the point wherex=
−3 andy=2, this is not the case. Both the -3 and the 2 arexvalues. This misconception is why you should
always writex∈because it reminds you of this fact. Many people get very confused when they see something like
x∈(− 2 , 1 )because they see the parenthesis and immediately see a point when they should see an interval on thex
axis.
Example C
Identify the domain and range of the following function.