Unit 2: 1 Functions
GOAL(S):
2015-2016: Algebra I CP
Represent relations and functions using tables, diagrams and graphs
Identify relations that are functions
LESKO’s Vending Machine
1
2
3
A
B
C
SOLD OUT
(1) What candy would you receive if you inserted money and pressed:
a. A2?
b. C3?
c. B1?
(2) Assuming the machine was filled properly; describe what would happen if you pressed the same button twice.
Each time you press a button, an INPUT, you may receive candy, an OUTPUT.
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Unit 2: 1 Functions
2015-2016: Algebra I CP
(3) In the candy machine, does every input have an output? Explain your response.
(4) Each combination of input and output can be expressed as a MAPPING DIAGRAM written input→output.
For example, B2 → Reeses Sticks.
a. Write a mapping diagram for each of the
b. Create a table to illustrate
possible combinations of buttons pushed
the inputs and outputs of the
and candy received in the vending machine.
vending machine are related.
Mapping Diagrams that relate values from one set to another set can be written as ORDERED PAIRS.
A RELATION is a set of ordered pairs. (input, output)
Relations can have a variety of representations. Consider the relation {(2, 5),(5, 9), (8, 1)}. The relation can also be
represented in the following three ways.
TABLE
x
MAPPNG
GRAPH
y
2 5
2
5
5 9
5
9
8 1
8
1
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Unit 2: 1 Functions
2015-2016: Algebra I CP
A FUNCTION is a relation in which every input is paired with exactly one output.
(5) Suppose when pressing button C1 on the vending machine both Swedish Fish and Peanuts come out. Describe how
this vending machine resembles or does not resemble a function.
(6) Create an example of a situation (math or real-life) that behaves like a function and another that does not behave
like a function. Explain why you chose each example to fit the category.
a. Behaves like a function
b. Does not behave like a function
(7) Determine whether each list of ordered pairs represents a function. Explain your answers.
a. {(5, 4), (6, 3), (7, 2)}
b. {(4, 5), (4, 3), (5, 2)}
c. {(5, 4), (6, 4), (7, 4)}
(8) Write two relations as lists of ordered pairs below, one that is a function and one that is not a function.
a. Function
b. Not a Function
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Unit 2: 1 Functions
2015-2016: Algebra I CP
(9) Does the table represent a function? Explain.
(10) Does the mapping diagram represent a function?
Explain.
x
y
-4 0
-3 3
-1
0
-2 5
1
-2 7
2
0
5
9
1
9
(11) Does the graph represent a function? Explain.
(12) Does the graph represent a function? Explain.
(13) Does the graph
represent a
function? Explain.
(14) Does the graph
(15) Does the graph
represent a
represent a
function?
function? Explain.
Explain.
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Unit 2: 1 Functions
2015-2016: Algebra I CP
Describe domain and range of a function
GOAL(S):
Find input-output pairs for a function.
The set of all inputs for a function is known as the DOMAIN of the function.
The set of all outputs for a function is known as the RANGE of the function.
(16) Using Mrs. Lesko’s vending machine.
a. Identify the domain
b. Identify the range
For each function below, identify the domain and the range.
(17)
(20)
Input Output
(18)
(19)
3
2
2
5
3
1
8
6
0
11
9
-1
14
-3
-5
(21)
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Unit 2: 1 Functions
(22)
2015-2016: Algebra I CP
(23)
(24) You are at the Jilly’s arcade on the boardwalk. They have a vending machine that exchanges your one dollar bill for
quarters. You are allowed to insert at most 5 one-dollar bills.
a. Think about the domain and the range of the machine. Can you list the domain and range?
b. Is 7 a possible input for the relation of this machine? Explain.
c. Could 3.5 be included in the domain of this relation? Explain.
d. What values are NOT in the domain? Explain.
e. Is 8 a possible output for the relation? Explain.
f.
Could 3 be included in the range of the relation? Explain.
g. What values are NOT in the range? Explain.
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Unit 2: 1 Functions
2015-2016: Algebra I CP
(25) Sometimes machine diagrams are used to represent functions. In the function machine below, the inputs are
labeled x and the outputs are labeled by y. In this case, the machine is named f. Machine names can be any name!
This machine will represent f(x) = 3x – 8
a. What is the output if the input is x = 7?
b. What is the output if the input is x = 1 ?
3
c. What is the input if the output is y = -11?
d. What is the input if the output is f(x) = -2?
(26) Use the new function machine to find the ordered pairs for the following values.
h
¾x +h 4
a) x = -4
b) x = 8
c) y = -2
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Unit 2: 1 Functions
2015-2016: Algebra I CP
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