LF.1 Domain and Range
TEACHER: Describing Domain & Range
Linear Functions Learning Targets
Practice 4. Model with mathematics.
Practice 6. Attend to precision.
A-CED.2 Create equations in two or more variables to represent relationships between
quantities; graph equations on coordinate axes with labels and scales. 
A.CED I can create equations that describe numbers or relationships.
A-CED.2
 Create equations with 2 variables to represent relationships between two quantities with
equations and tables.
 Graph equations on coordinate axes with labels and scales.
F-IFa I can understand the concept of a function and use function notation.
F‐IF.1 Understand that a function from one set (called the domain) to another set (called the
range) assigns to each element of the domain exactly one element of the range. If f is a
function and x is an element of its domain, then f(x) denotes the output of f corresponding to
the input x. The graph of f is the graph of the equation y = f(x). 
 Apply the definition of a function to determine if an equation, a table, or graph is a function.
 Know the graph of the function is the graph of all (x, f(x)) coordinate points.
A review of Number Systems will help us describe domains and ranges.
1. Identify the number system of each sequence.
a. 0, 2, 4, 6, …
whole numbers
b. 1, 2, 3, 4, …
counting numbers
c. 6, 5, 4, 3, …
integers
d. 1, -2, 4, -8, …
integers
e.
1 3 5 7
, , , ,...
2 2 2 2
rational numbers
f.
1 2 4
, ,1, ,...
3 3 3
rational numbers
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LF.1 Domain and Range
TEACHER: Describing Domain & Range
g.
2
3 2
, 2,
,2 2,...
2
2
irrational numbers numbers
h.
3 3 3 3 9
, ,
, ,...
2 4 8 16
real numbers
a(1)
a(2)
a(3)
2. Write an equation that can be used to find the nth term of the tile pattern sequence.
Equation: a(n) = 3n + 1
Define your variables: n is the term number; a(n) is the
number of tiles in the nth term.
3. Make a graph of the first 5 terms of the sequence.
4. Explain how you know whether or not the sequence is a function.
The sequence is a function because each term number has
only one possible number of tiles in it.
5. Describe the domain and range of the sequence.
Domain: natural numbers from 1 to 5
Range: 4, 7, 10, 13, 16
Lori has 1 dollar in her wallet. Her mother gives her $8 dollars every day for lunch at school.
This week, she spends $5 a day for lunch and puts the rest in her wallet to save to buy a CD she
wants.
6. Write an equation that can be used to find the money in her
wallet after lunch each day of the week.
Equation: y = 3x + 1
Define your variables: x is the number of days Lori has been
saving; y is the amount of money Lori has in our wallet
after lunch.
7. Make a graph to show how much Lori has in her wallet for each
of the days of the week.
8. Explain how you know whether or not the situation is a function.
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LF.1 Domain and Range
TEACHER: Describing Domain & Range
The sequence is a function because each day has only a unique amount of money in
Lori’s wallet.
9. Describe the domain and range of the situation.
Domain: natural numbers from 1 to 5
Range: 4, 7, 10, 13, 16
Benny planted a bean for science class. On Sunday when he first noticed the plant sprouted, it
was one centimeter tall. Each day after that the plan grows 3 centimeters each day. Every day
for the next week he recorded the height of the bean plant when he came home from school.
10. Write an equation that can be used to find the height of the
bean plant each day of the week.
Equation: y = 3x + 1
Define your variables: x is the number of days; y is the
height of the bean plant.
11. Make a graph to show how height of the bean plant for the
week.
12. Explain how you know whether or not the situation is a
function.
The sequence is a function because each day has only a
unique height of the bean plant.
13. Describe the domain and range of the situation.
Domain: real numbers from 1 to 5
Range: real numbers from 4 to 16
DEBRIEF
Use what you know about Number System to compare each of these
three situations:

equations The equations are the same: y = 3x + 1

graph The sequence and wallet graphs have the same
points plotted, but with different labels. The bean graph
is what you get if you connect all the points of the other
two graphs.

domains and ranges
The domains of the sequence and wallet graphs are integers 1 to 5. The bean domain
is real numbers from 1 to 15.
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LF.1 Domain and Range
TEACHER: Describing Domain & Range
The ranges of the sequence and wallet graphs are integers 4 to 16. The bean domain
is real numbers from 4 to 16.
BIG IDEA: Situations represented linear functions can have discrete or
continuous domains.
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