Vocabulary
Evaluating Function Rules
Independent & Dependent
Domain & Range
Is it a Function?
100
What is the definition of domain?
A set of input values (all values of x).
100
Evaluate f(2) if f(x)=-3x
f(2) = -6
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=f+20, where f is the number of minutes your friend spends studying, and y is the number of minutes you spend studying. Identify the independent and dependent variables.
Independent Variable: The number of minutes your friend spends studying.
Dependent Variable: The number of minutes you spend studying.
100
State the domain and range:
| x | y |
| 3 | 7 |
| 5 | 9 |
| 3 | 8 |
D: {3, 5}
R: {7, 8, 9}
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 range?
The set of output values (all values of y).
200
Evaluate f(7) if f(x)= -(4x+2)
f(7) = -30
200
Identify the independent variable: The relationship between the number of hours worked and the amount of money earned.
The number of hours worked.
200
State the domain and range:
D: {1, 2, 3, 4, 5, 6}
R: {-1, 0, 1, 2, 3, 6}
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
Evaluate f(-6) if f(x)=x^2 - 9
f(-6) = 27
300
Identify the dependent variable: The relationship between your allowance and the number of chores you do.
Your allowance.
300
x: 0, 1, 4
y: 2, 7, -1, 0
Domain: 0, 1, 4
Range: -1, 0, 2, 7
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
What is the definition of an independent variable?
A variable whose values affect the values of another variable (dependent variable). It is usually found on the x-axis of a graph.
400
Evaluate f(x)=9 if f(x)=25 - 4x
x = 4
400
Identify the independent and dependent variables: 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
x=-2
D: -2
R: all real numbers
400
Is it a function? Justify your answer.
%26x%3D0003&imgrefurl=http://www.algebra.com/algebra/homework/Coordinate-system/Coordinate-system.faq.question.24806.html&usg=__N8FQPaDH4lCUX1u24T4Y85yHJg0=&h=302&w=308&sz=8&hl=en&start=18&zoom=1&tbnid=QxN6mNRwuBZU7M:&tbnh=115&tbnw=117&ei=dJa7TY3pKaLz0gH9iYCwBg&prev=/search%3Fq%3Dlinear%2Bgraphs%26hl%3Den%26rls%3Dcom.microsoft:en-us:IE-SearchBox%26rlz%3D1I7TSNA_enUS397US397%26biw%3D1345%26bih%3D606%26site%3Dsearch%26tbm%3Disch&um=1&itbs=1)
Yes, it passes the Vertical Line Test.
500
What is the test to tell if a graph is a function?
Vertical Line Test
500
Evaluate f(x)=42 if f(x)=3x^2+15
x = 3 or -3
500
Identify the independent and dependent 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
The cost of purchasing 1, 2, 3, or 4 t-shirts from a souvenir shop is $10, $18, $24, and $28.
Domain: 1, 2, 3, 4
Range: 10, 18, 24, 28
500
Is it a function? Justify your answer.
Yes, each input has exactly one output.