Functions

Vocabulary

100

What is the definition of input?

All of the x values in a function.

200

What is the definition of output?

All of the y values of a function.

300

What is the definition of a function?

A relationship between input and output values. Each input has exactly one output value.

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)

500

What is the test to tell if a graph is a function?

Vertical Line Test

Independent & Dependent

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.

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.

300

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

Your allowance.

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.

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.

Interpreting Functions

100

Given this set of inputs and outputs, is the function increasing or decreasing? 

x	y
3	7
5	9
3	8

Increasing

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.

300

How do you find the initial value of a function? 

Look for the y-intercept or when x is zero.

400

At what (x,y) pair does the function start to decrease? 

(2,3)

500

Find the slope and y-intercept: 

2x + y = 4

slope: -2

y-intercept: 4

Is it a Function?

100

Is it a function? Justify your answer. {(2, 3), (4, 5), ( -2, 6)}

Yes, each input has exactly one output.

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

Is it a function? Justify your answer.

x	y
2	4
1	5
2	6

No, there are repeated inputs.

400

Is it a function? Justify your answer.

Yes, it passes the Vertical Line Test.

500

Is it a function? Justify your answer.

Yes, each input has exactly one output. It passes the vertical line test.