Vocabulary
Function Rules
Independent & Dependent
Towers
Is it a Function?
100

What is the definition of dependent variables?

a variable in a functional relationship that changes its value when a value of the independent variable is changed.

100

Sally has attended her school's annual carnival for two  years in a row.  This year's ticket prices for the rides are shown in the table.  Write the equation for this table

y=x +2 

100

You and a friend are studying for a quiz. You want to get a higher score than your friend, so you decide to spend exactly 20 more minutes studying than your friend does. The relationship between these two variables can be expressed by the equation y=x+20, where x is the number of minutes your friend spends studying, and y is the number of minutes you spend studying. Identify the independent (x) and dependent (y) variables.

Independent (x) Variable: The number of minutes your friend spends studying. Dependent (y) Variable: The number of minutes you spend studying.

100

How many faces will you need to paint if you have a 24-story tower?

97 faces 

100
Is it a function? Justify your answer. {(2, 3), (4, 5), ( -2, 6)}
Yes, each input has exactly one output.
200

What is the definition of an independent variable?

a variable in a functional relationship that determines what happens to another variable in the relationship.

200

Write an equation of the function for the table shown below:

y=3x

200

Identify the independent (x) variable: The relationship between the number of hours worked and the amount of money earned.

The number of hours worked.

200

How many faces will you need to paint on a 32-story tower?

129 faces

200
Using the vertical line test, does the graph of the points (1,3) and (1,5) represent a function?
No, the points fail the Vertical Line Test.
300
What is the definition of a function?
A relationship between input and output values. Each input has exactly one output value.
300

Given the points, write a function rule:

(0, 0); (2, 1); (4, 2)

y=1/2x

300

Identify the dependent (y) variable: The relationship between your allowance and the number of chores you do.

Your allowance.

300

If the tower you paint has 145 exposed faces, how many stories is the tower?

36 stories. 

300
Is it a function? Justify your answer.
x y
2 4
1 5
2 6
No, the input of 2 has two different outputs.
400

Which variable is the input, and which one is the output? 

(Which one is the x-variable, which one is the y-variable?)

x-variable is the input, y-variable is the output

(x - independent, y - dependent)

400

Given the points, write the rule:

(0, 5); (1, 6); (2, 7); (-1, 4)

y=x+5

400

Identify the independent (x) and dependent variables (y): You are buying boxes of cookies at a bakery. Each box of cookies costs $4.

Independent Variable: The number boxes of cookies purchased. Dependent Variable: How much you spend at the bakery.

400

If the tower you paint has 409 exposed faces ,how many stories is the tower?

102 stories

400
Is it a function? Justify your answer.
Yes, it passes the Vertical Line Test.
500
What is the test to tell if a graph is a function?
Vertical Line Test
500

Given the points, write the rule:

(-1, -1); (0, 1); (1, 3); (2, 5)

y=2x+1

500

Identify the independent (x) and dependent (y) variables: On your math quiz, you earn 5 points for each question that you answer correctly.

Independent Variable: Number of questions answered correctly. Dependent Variable: Score on the quiz.

500

A graph contains the point (15,61). What does this mean in the context of the tower-painting problems?

The tower with 15 cubes or stories will have 61 painted cube faces. 

500
Is it a function? Justify your answer.
Yes, each input has exactly one output.
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