Vocabulary
Independent & Dependent
Interpreting Functions
Is it a Function?
100
What is the definition of input?
All of the x values in a function.
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
Given this set of inputs and outputs, is the function increasing or decreasing?
| x | y |
| 3 | 7 |
| 5 | 9 |
| 3 | 8 |
Increasing
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 output?
All of the y values of a function.
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
Would this function fit a linear model? Why or why not? 
No because there isn't a constant rate of change between points -- it's not predictable.
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. There are repeated inputs.
300
What is the definition of a function?
A relationship between input and output values. Each input has exactly one output value.
300
Identify the dependent (y) variable: The relationship between your allowance and the number of chores you do.
Your allowance.
300
How do you find the initial value of a function?
Look for the y-intercept or when x is zero.
300
Is it a function? Justify your answer.
| x | y |
| 2 | 4 |
| 1 | 5 |
| 2 | 6 |
No, there are repeated inputs.
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
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
At what (x,y) pair does the function start to decrease?
(2,3)
400
Is it a function? Justify your answer.
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Yes, it passes the Vertical Line Test.
500
What is the test to tell if a graph is a function?
Vertical Line Test
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
Find the slope and y-intercept:
2x + y = 4
slope: -2
y-intercept: 4
500
Is it a function? Justify your answer. 
Yes, each input has exactly one output. It passes the vertical line test.