Download Notes on Domain/Range in Real-Life Functions

Notes on Domain/Range in Real-Life Functions
Name_______________________________
To begin, it is important for you to understand the meaning of the inequalities occasionally used to express the
domain and range of a function.
For example, suppose the domain of a function is 1  x  3 .
This means that the domain is every number from -1 to 3, including -1 and 3.
Suppose the domain of a function is x  7 .
This is the same as stating the domain is every number that is greater than 7.
--------------------------------------------------------------------------------------------------------------------- ----------------------Use words to express the range, if the range of a function is y  1 .
The range is ________________________________________________________________________________.
Use words to express the range, if the range of a function is. 4  y  11 .
The range is________________________________________________________________________________.
Recall the following function from the last night's homework, and recall its
graph to the right:
The number of hot dogs devoured by professional eater Kobayashi during the
11-minute contest is a function of time.
In a ______________________ function (like this function),
discrete or continuous???
the domain and range are usually expressed as inequalities. If you can change
these inequalities to words (as we did above), you only need to add
the units of the real-life problem. THE UNITS ARE VERY IMPORTANT!
Number of hot dogs
--------------------------------------------------------------------------------------------------------------------- ----------------------Like all other functions, real-life functions have a domain and range as well.
Time
What is the domain of this function? Express using inequalities.
Now, use words to express the domain:
The domain is any time, in minutes, beginning at _____ and ending at _____.
Use words to express the range:
The range is any number of hot dogs, starting at _____ and ending at ___________________________________.
Note that the only real difference in these "words" and the ones at the top of the page is the use of the real-life
quantity (time, hot dogs), instead of the word "number".
--------------------------------------------------------------------------------------------------------------------- ----------------------Use words to express the domain and range of this function --- approximate if necessary: the height of a golf ball
above the ground during one golf shot is a function of the time since the golf ball was hit.
Use words to express the domain and range of this function --- approximate if necessary: the height of the average
male who lives for 100 years is a function of time since birth up until death.
Homework on Domain/Range in Real-Life Functions
Name_______________________________
For Questions 1-6, are the given functions discrete or continuous? Then, state the domain and range.
1.
2.
3.
6
6
6
4
4
4
2
2
2
-5
5
-5
5
-5
5
-2
-2
-2
-4
-4
-4
-6
-6
-6
4.
5.
6.
6
6
6
4
4
4
2
2
2
-5
5
-5
5
-5
5
-2
-2
-2
-4
-4
-4
-6
-6
-6
--------------------------------------------------------------------------------------------------------------------For Questions 7-9, use words to state the domain and range of the functions described below. Approximate any
numbers as needed (like the maximum height of the golf ball was approximated).
7.
In an effect to show evidence of global warming: the highest temperature of the year in Macon, Georgia
is a function of any year since 1900. For this question, just fill in the blanks.
The domain is any year from _________ to __________.
The range is any ____________________ from __ 96 __ to __ 114 __.
8.
The number of A's on a high school student's nine weeks' report card is a function of the number of
absences the student had during those nine weeks.
The domain is _________________________________________________________________________.
The range is ___________________________________________________________________________.
9.
The height above the water of a diver jumping off of the "high dive" at a swimming pool is a function of
the time since jumping until the time the person comes to the surface to breathe.
The domain is any time, in seconds, ________________________________________________________.
The range is ___________________________________________________________________________.
----------------------------------------------------------------------------------------------------------------------------- --------------1. continuous; D:
R: y  2
2. discrete;
D: {3}
R: {4}
3. continuous;
D: 2  x  0
R: 3  y  6
4. discrete;
D: {-3,1,2,3,6} R: {-3,-2,2,3}
5. continuous;
D:
R:
6. continuous;
D: 3  x  6
R: 1  y  5