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Deep and Wide:
Domain & Range
TEKS A.2B The student is expected to
identify mathematical domains and ranges
and determine reasonable domain and
range values for given situations, both
continuous and discrete

A function is a set of ordered pairs of
numbers (x, y) such that no x –values
are repeated.

What are the domain and range of a
function?

The domain and range of a function
are sets that describe those ordered
pairs.
Definition
Domain All the x-coordinates in
the function's ordered
pairs
Range
All the y-coordinates in
the function's ordered
pairs
Example
{(3, 6), (2, 8), (5,
3)}
{ 3, 2, 5}
{ 6, 8, 3}
The domain is the set of all the values of
the independent variable, the xcoordinate
The range is the set of all the values of
the dependent variable, the ycoordinate.
Identify the domain and range of the
function below.
{ 2, 7), (4, 11), (6, 15), (8, 19)}

The domain is { 2, 4, 6, 8}

The range is { 7, 11, 15, 19}
Graphs

The domain of a function is the set of all
the x-coordinates in the functions’ graph
Domain
3 ≤ x ≤ 12
The range of a function is the set of all the ycoordinates in the functions’ graph
Range 6 ≤ y ≤ 12
What is the domain of this function?
What is the range of this function?
Domain is 0 ≤ x ≤ 4
Range is 1 ≤ y ≤ 5
The graph shows the path of a golf ball
What is the range
of this function?
F 0 < y < 100
G 0 ≤ y ≤ 100
H 0≤x≤5
J 0≤x≤5
What is the domain of this function?
A -1 ≤ x ≤ 5
B -1 ≤ x ≤ 9
C 2≤x≤5
D 0≤ y≤ 9
What is the domain of the function
shown on the graph?
A -2 < y ≤ 2
B -4 ≤ x ≤ 6
C -4 < y ≤ 2
D -2 < x ≤ 6
Sometimes you will be asked to
determine a REASONABLE domain
or range
The average daily high temperature for the
month of May is represented by the function
t = 0.2n + 80
Where n is the date of the month. May has 31
days. What is a reasonable estimate of the
domain?
Answer: 1 ≤ n ≤ 31
What is a reasonable estimate of the range
Answer: See next slide
Our function rule is:
t = 0.2n + 80
Our domain is 1 ≤ n ≤ 31
Our smallest possible n is 1
Our largest possible n is 31
To find the range, substitute 1 into the equation
and solve. Then substitute 31 into the
equation and solve.
Our function rule is:
t = 0.2n + 80
Substitute a 1
t = 0.2n + 80
t = 0.2(1) + 80
t = 0.2 + 80
t = 80.2
Substitute a 31
t = 0.2n + 80
t = 0.2(31) + 80
t = 6.2 + 80
t = 86.2
Reasonable range is 80.2 ≤ t ≤ 86.2