1 / 15

Relations and Functions

Relations and Functions. June 21, 2012. What is a Relation?. A relation is a set of ordered pairs. When you group two or more points in a set, it is referred to as a relation. When you want to show that a set of points is a relation you list the points in braces.

yosef
Télécharger la présentation

Relations and Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Relations and Functions June 21, 2012

  2. What is a Relation? A relation is a set of ordered pairs. When you group two or more points in a set, it is referred to as a relation. When you want to show that a set of points is a relation you list the points in braces. For example, if I want to show that the points (-3,1) ; (0, 2) ; (3, 3) ; & (6, 4) are a relation, it would be written like this: {(-3,1) ; (0, 2) ; (3, 3) ; (6, 4)}

  3. Domain and Range • Each ordered pair has two parts, an x-value and a y-value. • The x-values of a given relation are called the Domain. • The y-values of the relation are called the Range. • When you list the domain and range of relation, you place each the domain and the range in a separate set of braces.

  4. For Example, 1. List the domain and the range of the relation {(-3,1) ; (0, 2) ; (3, 3) ; (6, 4)} Domain: { -3, 0, 3, 6} Range: {1, 2, 3, 4} 2.List the domain and the range of the relation {(-3,3) ; (0, 2) ; (3, 3) ; (6, 4) ; ( 7, 7)} Domain: {-3, 0, 3, 6, 7} Range: {3, 2, 4, 7} Notice! Even though the number 3 is listed twice in the relation, you only note the number once when you list the domain or range!

  5. What is a Function? A function is a relation that assigns each y-value only one x-value. What does that mean? It means, in order for the relation to be considered a function, there cannot be any repeated values in the domain. There are two ways to see if a relation is a function: • Vertical Line Test • Mappings

  6. Use the vertical line test to check if the relation is a function only if the relation is already graphed. Hold a straightedge (pen, ruler, etc) vertical to your graph. Drag the straightedge from left to right on the graph. 3. If the straightedge intersects the graph once in each spot , then it is a function. If the straightedge intersects the graph more than once in any spot, it is not a function. A function! Using the Vertical Line Test

  7. Examples of the Vertical Line Test function Not a function Not a function function ……….

  8. Mappings If the relation is not graphed, it is easier to use what is called a mapping. • When you are creating a mapping of a relation, you draw two ovals. • In one oval, list all the domain values. • In the other oval, list all the range values. • Draw a line connecting the pairs of domain and range values. • If any domain value ‘maps’ to two different range values, the relation is not a function. It’s easier than it sounds 

  9. Example of a Mapping Create a mapping of the following relation and state whether or not it is a function. {(-3,1) ; (0, 2) ; (3, 3) ; (6, 4)} Steps Draw ovals List domain List range Draw lines to connect -3 0 3 6 1 2 3 4 This relation is a function because each x-value maps to only one y-value.

  10. Another Mapping Create a mapping of the following relation and state whether or not it is a function. {(-1,2) ; (1, 2) ; (5, 3) ; (6, 8)} -1 1 5 6 Notice that even though there are two 2’s in the range, you only list the 2 once. 2 3 8 This relation is a function because each x-value maps to only one y-value. It is still a function if two x-values go to the same y-value.

  11. Last Mapping Create a mapping of the following relation and state whether or not it is a function. {(-4,-1) ; (-4, 0) ; (5, 1) ; (3, 9)} Make sure to list the (-4) only once! -1 0 1 9 -4 5 3 This relation is NOT a function because the (-4) maps to the (-1) & the (0). It is NOT a function if one x-value go to two different y-values. ……….

  12. Vocabulary Review • Relation: a set of ordered pairs. • Domain: the x-values in the relation. • Range: the y-values in the relation. • Function: a relation where each x-value is assigned (maps to) on one y-value. • Vertical Line Test: using a vertical straightedge to see if the relation is a function. • Mapping: a diagram used to see if the relation is a function. ……….

  13. Complete the following questions: 1. Identify the domain and range tell whether if the relation is a function or not: a.{(-4,-1) ; (-2, 2) ; (3, 1) ; (4, 2)} b. {(0,-6) ; (1, 2) ; (7, -4) ; (1, 4)} 2. Use Vertical line test to tell whether if the relation is a function or not: 3. Use a mapping to see if the following relations are functions: a. {(-4,-1) ; (-2, 2) ; (3, 1) ; (4, 2)} b. {(0,-6) ; (1, 2) ; (7, -4) ; (1, 4)}

  14. -4 -2 3 4 0 1 7 -1 2 1 -6 2 -4 4 Answers (you will need to hit the spacebar to pull up the next slide) 1a. Domain: {-4, -2, 3, 4} Range: {-1, 2, 1} 1b. Domain: {0, 1, 7} Range: {-6, 2, -4, 4} 2a. 2b. 3a. 3b. Function Not a Function Not a Function Function

  15. Functions or Relations? • A={(2, -1), (4, 2), (6, 3), (8, 4)} • B={(3, -1), (3, -2), (1, -3), (0, -4)} • C={(-1, 2), (-2, 1), (-3, 0), (-4, -1)} 4. 5. 6.

More Related