Pre-Calculus/Trigonometry3
Name: ____________________________
Domain and Range
Notes Sheet
Interval Notation
Open Brackets:
Closed Brackets:
Mixed Brackets 1:
Mixed Brackets 2:
Example
x5
x5
0 x5
0 x5
(
[
(
[
,
,
,
,
)
]
]
)
means endpoints are not included in the set
means endpoints are included in the set
means minimum is not included; maximum is included
means minimum is included; maximum is not included
Set
All x-values less than 5 not including 5
All x-values less than and including 5
All x-values between (but not including) 0 and 5
All x-values between 0 and 5 including 0
Interval Notation
(-∞, 5)
(-∞, 5]
(0, 5)
[0, 5)
Increasing, Decreasing, and Constant Intervals & Relative Maximum/Minimum Values
increasing interval –
decreasing interval –
constant interval –
relative minimum value –
relative maximum value –
Domain - the set of all x-values for which a function is defined
Range - the set of all y-values for which a function is defined
To Define the Domain of a Function (Algebraically)
Case 1: Polynomial
f ( x)  4 x 3  x 2  5 x  1
Case 2: Fraction
5x  9
g ( x) 
6  2x
Case 3: Square Root
h( x )  4  x 2
To Define the Domain and Range of a Function (Graphically)
 To define the domain, read the graph from left (-∞) to right (∞) along the x-axis.
Use interval notation beginning with the first x-value that is defined for the graph.
 To define the range, read the graph from bottom (-∞) to top (∞) along the y-axis.
Use interval notation beginning with the first y-value that is defined for the graph.
 Any holes (open circles) or parts of the graph without x or y-values (gaps) are not
in the domain or range of the function.
Example: Define the Domain and Range of Graph A. Graph B and C may be helpful.
Graph A
Graph B
Domain: ___________________
Use the analogy of a “little man”
walking along the graph.
Graph C
Range: ____________________
Use the analogy of a “scanner”
and use pencils to scan from
bottom to top