Unit 2c – Algebraic Thinking –
Algebraic Functions
Class Notes
Date
Dependent and Independent Variables
Learning Target: I can use variables to represent two quantities in real-world problems.
I can distinguish between dependent and independent variables.
Key Terms


Dependent Variable: A variable in a functional relation whose value is determined by the value
or values of other variables. This variable depends on the other. When graphing, this is your y
coordinate.
Independent Variable: A variable whose value determines the value of other variables. When
graphing, this is your x coordinate.
Examples
In the following scenarios, identify the two variables you would use and what they represent.
The number of bicycles in the garage and the number of bicycle wheels in the garage.
b=number of bicycles
w= number of bicycles wheels
In the following scenarios, identify the independent and dependent variables.
The number of hours you worked last week and your paycheck.
Independent: hours worked
Dependent: paycheck
Try This
In the following scenarios, identify the two variables you would use and what they represent.
1) The temperature outside is 15° colder than the temperature inside the house.
2) The population of New York is twice as large as the population of Michigan.
In the following scenarios, identify the independent and dependent variables.
1) The cost of the birthday party and the number of kids attending.
2) The number of students attending the field trip and the number of buses taking them.
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Date
Function Tables
Learning Target: I can create a table to show the relationship between two variables.
Key Terms



Function: An input-output relationship that has exactly one output for each input.
Input: The value substituted into an expression or function. (Independent Variable)
Output: The value that results from the substitution of a given input into an expression or
function. (Dependent Variable)
Examples
Input
x
Rule
4x - 1
Output
y
1
4(1)-1
3
2
4(2)-1
7
3
4(3)-1
11
4
4(4)-1
15
Input
x
Rule
x³ - 6
Output
y
Rule
10x ÷ 5
Output
y
Try These
1)
2
4
6
8
2)
Input
x
5
10
15
20
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Page 2
Date
Graphing Functions
Learning Target: I can graph the relationship between two variables.
Key Terms

Function Table: A table of ordered pairs that represent solutions to a function.
Example:
Function Rule
y = 3x +1
Output
y
Ordered
Pair
(x,y)
0
3(0)+1
1
(0,1)
1
3(1)+1
4
(1,4)
2
3(2)+1
7
(2,7)
3
3(3)+1
10
(3,10)
Output
y
Ordered
Pair
(x,y)
Input
x
Try This:
Input
x
Function Rule
y = 2x +3
0
1
2
3
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Page 3
Date
Function Rules
Learning Target: I can write a function rule (equation) to show the relationship between two variables.
Key Terms

Function Rule: An equation that describes the relationship between the input (x-value) and the
output (y-value) in a function.
Steps for Writing a Function Rule
1. Look for a pattern in both the input and the output columns. This is your change in x and
change in y.
2. Divide your change in y (output) by your change in x (input). This becomes the coefficient of x in
your function rule.
3. Pick one of your x values and multiply it by the coefficient of x that you found in step 2. Decide
if you need to add or subtract and by how many to get the y value. This number becomes the
constant in your function rule.
Try This
1)
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2)
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Date
Function Word Problems
Learning Target: I can solve real-world problems involving functions.
Example:
Dan had to have his home computer serviced. The service company charges $55 just to come to his
house. They then charge $150 an hour. Create a function table to show how much it would cost to fix a
computer that took 4, 8 and 12 hours to fix. Using that table, what is the function rule used to
determine the overall cost?
Table
(hours)
4
8
12
Function Rule: y = 150x + 55
(cost)
655
1255
1855
Try This:
1) Ockerman Middle School is planning on taking a field trip to the movies. The cost depends on how
many students attend. If 35 students go the cost is $230, if 70 students go the cost is $510, if 105
students go the cost is $790 and if 140 students go the cost is $1070. First, create an input/output table
displaying this information. Then using that table, what is the function rule?
2) At Pete’s Pizza Palace you can get a variety of 13 different types of toppings on your pizza. Your
price depends on how many toppings you choose. A medium, 1-topping pizza will cost you $8.00, a
medium 3-topping pizza will cost you $11.50 and a medium 5-topping pizza will cost you $15.00. Create
a function table to show the relationship between cost and toppings. Using that table, find the function
rule. Using that function rule, how much wills a medium pizza cost with all 12 toppings?
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3) Your parents bought you a cell phone for your birthday. With their plan, you only get a limited
number of texts each month. If you go over, it costs your parents an additional amount each month.
The first month you went over by 10 texts and your parent’s bill was $54.99. The second month you
went over by 30 texts and the cost was $64.99. During the third and fourth months you continue to go
over by 50 then 70 texts! During those two months it cost you parents $74.99 and $84.99. First create
an input/output table showing the relationship between cost and your number of texts. Using the table,
determine the function rule. How much do your parents pay each month, regardless of how many texts
you send? How much extra does it cost them for each text you are over?
4) A plain hamburger costs $2.99. You can buy additional toppings for $0.55 each. What will a
hamburger with 5 toppings cost? Create a table to solve and include the function rule.
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