Pre Calc Flashcards
What is the heart of Precalculus?
The study of functions
Functions relate a set of input values to a set of output values.
How do we denote that y is a function of x?
y = f(x)
This notation indicates that y is dependent on the variable x.
What variable is commonly used in function notation?
f
Other letters such as g and h can also be used to describe functions.
In a function P = m, what do P and m represent?
P is the number of points fallen; m is the amount of medication taken
This is an example of using function notation in a practical scenario.
What is the domain of a function?
The set of allowable input values
This defines the values that can be used as inputs in a function.
What is the range of a function?
The set of allowable output values
This defines the possible outputs that can result from the function.
Fill in the blank: The time to fill a bathtub is a function of the _______.
rate that water comes from the faucet
Fill in the blank: The temperature of a broiler is a function of the _______.
amount of time it is heated
What is the function definition regarding the domain and range?
For every r in the domain, there can only be one and only one y in the range
This means no x-value can repeat, but y-values can.
True or False: In a function, it is possible for x-values to repeat.
False
Each x-value must correspond to only one y-value.
Provide an example of a domain for a bathtub function.
Values between 0 and 2 gallons per minute
This indicates the rate of water flow that is allowed for the function.
What is an example of a range for a broiler function?
Values between 0 and 550°F
This shows the output temperatures that can be reached by the broiler.
What is the definition of a function?
In a function, for every x in the domain, there can only be one and only one y in the range.
Can y-values repeat in a function?
Yes, y-values can repeat, but x-values cannot.
What is the domain in the context of a school locker example?
The domain is the set of students in the school.
What is the range in the context of a school locker example?
The range is the lockers numbered.
What happens if two students are assigned to the same locker?
The y-value (locker number) repeats, which is allowable in a function.
What is a problem if a student is assigned to multiple lockers?
It creates ambiguity about which locker contains their possessions.
What happens if a student is not assigned a locker?
The student is a valid member of the domain, but there is no corresponding y-value, which causes a problem.
How can functions be expressed?
Functions can be expressed graphically, verbally, and analytically.
What is an example of a verbal expression of a function?
Steve’s allowance.
What is an example of restricting the domain of a function?
A market sells deli cheese at $6.00 a pound, but a customer is restricted to only 3 pounds.
