Function Concepts
What is the definition of a function?
A function gives the distance a person walks, in miles, as a function of the time t they spend walking, in minutes.
Using function notation, represent a person walking 1 mile in 15 minutes
f(15)=1
A function gives the distance a person walks, in miles, as a function of the time t they spend walking, in minutes.
What does f(8) = 1 mean in the context of our function?
A person has walked 1 mile over the course of 8 minutes
Is every input and every output possible for every function? Why or why not?
No! It depends on the context of the function - what are the restrictions on the independent and dependent variables?
Which state is Mr. K originally from?
Wisconsin
What is the correct notation for a function of x?
f(x)
A function gives the distance a person walks, in miles, as a function of the time t they spend walking, in minutes.
Using function notation, represent a person walking 3.5 miles in 65 minutes
f(65)=3.5
A function gives the distance a person walks, in miles, as a function of the time t they spend walking, in minutes.
What does f(3.5) = 42 mean in the context of our function?
A person has walked 3.5 miles over the course of 42 minutes
A function f(t) represents the distance a car travels as a function of the time t , in minutes, spent driving.
Is 10 a possible input for this function?
Yes
This represents driving for 10 minutes
What is Mr. K's favorite sports team?
Green Bay Packers
Which variable do we use for the input of a function?
x (independent variable)
A function gives the cost of a taxi ride, in dollars, as a function of the distance d they drive, in miles.
Using function notation, represent a 2 mile ride that costs $10
f(2)=10
A function gives the cost of a taxi ride, in dollars, as a function of the distance d they drive, in miles.
What does f(2) = 10 mean in the context of the function?
A 2 mile taxi ride cost $10
A function f(t) represents the distance a car travels as a function of the time t , in minutes, spent driving.
Is 0 a possible input for this function?
Yes
This represents driving for 0 minutes (the very beginning of the drive!)
How old is Mr. K?
28
What variable do we use for the output of a function?
y (dependent variable)
A function gives the cost of a taxi ride, in dollars, as a function of the distance d they drive, in miles.
Using function notation, represent a 8.3 mile ride that costs 56 dollars and 25 cents
f(8.3)=56.25
A function gives the cost of a taxi ride, in dollars, as a function of the distance d they drive, in miles.
What does f(10.5) = 85.75 mean in the context of the function?
A 10.5 mile taxi ride costs $85.75
A function f(t) represents the distance a car travels as a function of the time t , in minutes, spent driving.
Is -1.5 a possible input for this function?
No
It is impossible to drive for a negative amount of time (we cant time travel!)
What is Mr. K's cat's name?
Chad
Can a function have more than 1 output per input? Why or why not?
No; it would no longer be a function!
A function gives the amount of water, in liters, a water tank loses due to evaporation as a function of the time t after the tank is filled, in hours.
Using function notation, represent a water tank losing 2.5 liters of water to evaporation 36 hours after it was filled
f(36)=2.5
A function gives the amount of water, in liters, a water tank loses due to evaporation as a function of the time t after the tank is filled, in hours.
What does f(12) = 1.5 mean in the context of the function?
A water tank has evaporated 1.5 liters of water over the course of 12 hours (after it was filled)
A function f(t) represents the distance a car travels as a function of the time t , in minutes, spent driving.
Is 1,000 a possible output for this function?
Yes
This represents traveling 1,000 miles (that's a long drive, but its possible!)
What is Mr. K's wife's name?
Annika