Domain & Range
| Site: | St. Louis |
| Course: | Michigan Algebra I Sept. 2012 |
| Book: | Domain & Range |
| Printed by: | Guest user |
| Date: | Sunday, April 28, 2024, 9:44 AM |
Description
Domain
The domain of a function is the set of values of the independent variable (x) for which the function is defined.
There are two common mathematical operations that are undefined: square root of a negative number and division by zero. Since linear functions do not include either of these operations, their domain is usually all real numbers.
If the value of x is not restricted by the situation the function is modeling, then the domain can be defined as all real numbers. This is written 
. The domain will provide the x coordinates for the function graph.
Examples
Example 1 What is the domain of the function y = 4x -2 ?
. Example 2 What is the domain of the function f(t) = 3t - 4 , where t represents the time it takes to wash a car in minutes?
Since the domain is modeling time, it will be restricted to numbers greater than or equal to 0 minutes, in set notation 
.
Range
The range of a function is the set of values of the dependent variable, y, for which the function is defined. If y is not restricted by the situation it is modeling, then it is defined as all real numbers and is written 
. The range provides the y coordinates for the function's graph.
Examples
Example 1 What is the range of the function y = 4x -2 ?
. Example 2 What is the range of the function f(t) =3t -4 , where t represents the time it takes to wash a car in minutes and f(t) represents the number of cars washed?
Since the range is modeling the number of cars, it will be restricted to numbers greater than or equal to 0 cars and will not be a fraction or decimal, in set notation 
.
Example 3 What is the range of the function y = 4?
Since the graph of this function will always have the output value of 4, its range is the number 4, in set notation 
.
Ordered Pairs
When given only a set of ordered pairs, the domain, x, and range, y, will correspond to just those coordinates.
Example Write the domain and range in set notation for the ordered pairs (2,1), (3, 2), (7, -1), (6, 4).
Domain: {2, 3, 6, 7}
Range: {-1, 1, 2, 4}
Notation
Domain and range are sometimes expressed as intervals. Use the open parentheses if the domain and range exclude the starting and ending values. Use square brackets [ ] if the domain and range include the starting and ending values.
Examples
1. (-3, 5) ? All numbers between -3 and 5, not including -3 and 5. ? ?3 < x < 5
2. [-3, 5] ? All numbers between -3 and 5, including -3 and 5. ? ?3 ? x ? 5
3. [-3, 5) ? All numbers between -3 and 5, including -3 but not 5. ? ?3 ? x < 5
4. (-?, 10]? All numbers less than or equal to 10. ? x ?10
5. (-?, 4) (4, ?) ? All numbers less than 4, and all numbers greater than 4. In other words, all numbers except 4. ? x ? 4
Videos
To learn more about domain and range, watch the following videos:
Practice
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Answer Key
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Sources
Embracing Mathematics, Assessment & Technology in High Schools; A Michigan Mathematics & Science Partnership Grant Project
Felder, Kenny "Function Concepts -- Domain and Range," Connexions, December 30, 2008, http://cnx.org/content/m18191/1.2/
Stapel, Elizabeth. "Functions: Domain and Range." Purplemath. Available from http://www.purplemath.com/modules/fcns2.htm. Accessed 14 August 2010
Tutor Vista, "Learn Online: History of Linear Functions ." 2010.http://www.tutorvista.com/math/learn-online-history-of-linear-functions (accessed 08/21/2010).