Vocabulary
Evaluating Function Rules
Independent & Dependent
Rate of Change
Is it a Function?
100
What is the definition of domain?
A set of all possible 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=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
A city has a population of 1 million in 2010, and 2 million in 2020. The rate of change is ____.
+100,000 people per year
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 (x) variable: The relationship between the number of hours worked and the amount of money earned.
The number of hours worked.
200
The formula for rate of change, in function notation.
(f(b)-f(a))/(b-a)
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 (y) variable: The relationship between your allowance and the number of chores you do.
Your allowance.
300
An empty bath tub is filled from time t=0 sec, to time t=10 sec. At ten seconds, the bath tub has 10 gallons of water. Then the bathtub is emptied. At t=15 seconds, the bathtub has 5 gallons of water. The average rate of change of the water in the bathtub from 0 to 15 seconds is ______.
1/3 gallons per sec.
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
Evaluate f(x)=9 if f(x)=25 - 4x
x = 4
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
State the average rate of change from x =2 to x =3. 
m = -3
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
Evaluate f(x)=42 if f(x)=3x+15
x = 9
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
Company A offers a phone plan that is always $50 per month. Company B offers a phone plan that has a flat fee of $10 per month, but each GB of data costs $5. In order for plan A to be the better deal a customer would have to use this number of GBs, per month.
More than 8.
500
Is it a function? Justify your answer.
Yes, each input has exactly one output.