Algebra 1 Unit 3 Note Sheets
OC4-1 Discrete Linear Functions Notes
1 EXPLORE Analyzing a Discrete Real-World Function
You buy a printer for $80 and then pay $15 for each ink cartridge that you use. A function relating the cost,
C (in dollars), of operating the printer to the number of cartridges used, n, is C(n) = 15n + 80.
A
Complete the table to represent the total cost for 0 to 4 cartridges.
Number
of
Cost, C
cartridges, (dollars)
n
0
1
2
3
4
B
Graph the function from Part A. Specify the scale you use.
C What is the initial value of the cost function? What does it represent?
What number of cartridges corresponds to the initial cost?
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D Compare the differences in cost with each unit increase in the number of cartridges purchased.
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Algebra 1 Unit 3 Note Sheets
REFLECT
1a. Identify the domain and range for the function C(n) using set notation.
Domain:
___
_________
Range:
1b. Describe the pattern formed by the points in the graph.
__
_________
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1c. How do your answers change if the price of the printer is $90?
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2 ENGAGE Recognizing Linear Functions
A function whose output values have a common difference for each unit increase in the input values is a
linear function. A linear function can be represented by the equation f(x) = mx + b, where m and b are
constants. The graph of a linear function forms a straight line.
When a linear function is discrete, its graph consists of isolated points along a straight line. If a discrete
linear function has inputs that are a set of equally spaced integers, then its outputs are a sequence of
numbers called an arithmetic sequence.
REFLECT
2a. Give three reasons why the cost function in the Explore is linear.
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2b. What are m and b and what do they represent for the cost function?
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