Functions
Function Notation
Graphs of Functions
Domain and Range
Construct Exponential Functions
100
Amber's classroom is hot, so she turned the air one. If the input is hours and the output is temperature. Which variable is the independent and which is the dependent?
The independent is the hours and the dependent is the temperature.
100
Function d gives the distance, in kilometers, after biking for h hours. What is the meaning of the equation d(2)=10?
After 2 hours, the biker has gone 10 miles.
100
What do we call the starting point of a graph on the y-axis?
What is the vertical intercept?
100
When asked what the domain is, are we looking at the x-values or the y-values?
What are the x-values?
100
If the number of points you get for a correct answer doubles each round, write an equation that shows the number of points a question is worth after x rounds.
p = 2x
200
How do we determine if a statement is a function?
The statement has one output for every input.
200
When given the function f(x) = 2, and we are told to find f(x), are we looking for the x value when y is 2 or the y-value when x is 2?
The x value when y is 2.
200
What do we call the point where our graph touches the x-axis?
What is the horizontal intercept?
200
When asked about the range of a function, are we looking at the x-values or the y-values?
What are the y-values?
200
If something is being doubled or tripled, what is this called?
What is a growth factor?
300
If given the statement C(10:15) = Math, what is the input and the output of the statement?
The input is 10:15 /time
The output is Math/class
300
Function P gives the population of Philadelphia (in billions) y years after 2000.
What does P(10) represent?
P(10) represents the population of Philadelphia (in billions) in 2010.
300
Which function value is greater g(2) or f(2)?
What is g(2)?
300
What is the domain of the function?
Domain: [-4, 3]
all real numbers from -4 to 3.
300
Pike wants to expand. Right now there are 2 Pike schools and their plan is to quadruple the number of schools each year for the next few years.
Write an equation representing the relationship between "x" years and "y" number of schools.
y = 2 x 4x
400
The monthly cost of a phone plan is represented by function P, defined by P(x) = 20x+15, where x is the hours of phone calls. Find P(x) = 120.
120 = 20x + 15
105 = 20x
5.25 = x
What is 5.25 hours of phone calls?
400
An art museum opens at 9 am and closes at 5pm. The function V given the number of visitors in a museum h hours after opening.
Explain what the statement V(1.25)=28 represents.
There are 28 visitors in the museum 1.25 hours after opening.
400
What values of x when f(x) = g(x)?
What is x = 1.5?
400
A gym is offering a special membership discount. Members pay $30 per entrance for the first 3 visits, and then after that get free entrance for the summer, up to 15 trips. The function C gives the total cost, in dollars, for a member to go to the gym n times.
What is the domain of function C?
What is all numbers between 0 and 15?
400
Rewrite the expression as a power of 2
23 x 24 x 22
29
500
The monthly cost of a phone plan is represented by function P, defined by P(x) = 20x+15, where x is the hours of phone calls. Find P(1.5).
20(1.5) + 15
30 + 15
45
What is $45?
500
The museum opens at 9am and closes at 5pm. The function V gives the number of visitors in a museum h hours after it opens. Use Function Notation to represent the following situation.
At 1pm, there were 257 visitors in the museum.
V(4) = 257
500
What is f(x) = 2?
What is f(-3) = 2?
500
A gym is offering a special membership discount. Members pay $30 per entrance for the first 3 visits, and then after that get free entrance for the summer, up to 15 trips. The function C gives the total cost, in dollars, for a member to go to the gym n times.
What is the range of function C?
The range includes multiples of 30 up to 90
500
Fred has two savings accounts:
Account A represents the amount of money after y years: A = 40(3)y
Account B represents the amount of money after y years: B = 4(4)y
Which savings account starts with more money?
Which savings account grows at a quicker rate?
Account A starts with more money but Account B grows at a quicker rate.