1 / 16

Relations

Relations. A relation is a set of ordered pairs. The first coordinates ( x ) are the domain of the relation. The domain contains all values of the independent variable .

kyle
Télécharger la présentation

Relations

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 • A relation is a set of ordered pairs. • The first coordinates (x) are the domain of the relation. The domain contains all values of the independent variable. • The second coordinates (y) are the range of the relation. The range contains all values of the dependent variable.

  2. Variables • Independent Variable: The variable in a relation whose value is subject to choice. • Dependent Variable: The variable in a relation whose value depends on the value of the independent variable. • What examples can you think of where one thing depends on another?

  3. Domain Independent Variable x-axis First coordinates Range Dependent Variable y-axis Second coordinates Vocabulary Summary Chart (x, y)

  4. Functions • Some relations are functions. • In a function, each member of the domain is paired with exactly one member of the range. • x values can only go with one y • y values can go with any number of x values

  5. Inverses • The inverse of any relation is obtained by switching the coordinates in each ordered pair.

  6. Representations • A relation can be represented in different ways, such as a • Set of ordered pairs • Table • Graph – Review Coordinate Plane Vocabulary • Mapping

  7. X 4 -2 -3 2 0 Y 3 -1 2 -4 Mapping • A mapping is an easy way to determine if a relation is a function. • Remember if your x goes to more than one y, then it is not a function. • A mapping for the ordered pairs : (4, 3) (-2, 1) (-3, 2) (2, -4) (0, -4)

  8. Example 1a: List the domain and range for each relation. Is each relation a function? Explain. Make a t • (0, 5), (1, 6), (2, 4), (3, 7) Domain: ____________ Range: ____________

  9. Example 1b: List the domain and range for each relation. Is each relation a function? Explain. • (0, 5), (1, 5), (2, 6), (3, 7) Domain: ____________ Range: ____________

  10. Example 1c: List the domain and range for each relation. Is each relation a function? Explain. • (0, 5), (0, 6), (1, 6), (2, 7) Domain: ____________ Range: ____________

  11. Express the relation {(4, 3), (–2, –1), (–3, 2), (2, –4), (0, –4)} as a table, a graph and a mapping.

  12. a. Express the relation {(3, –2), (4, 6), (5, 2), (–1, 3)} as a table, a graph, and a mapping. b. Determine the domain and range. c. Write the inverse of the relation.

  13. Graphing & the Vertical Line Test • Graphing a relation on a coordinate plane gives us a visual way to tell whether the relation is a function. • Vertical Line Test • If a vertical line can be drawn so it intersects the graph at two or more points (at the same time), then the relation is not a function.

  14. Example 3a: Graph the relation shown in the table. Is it a function? Explain.

  15. Example 3b: Graph the relation shown in the table. Is it a function? Explain.

  16. Summary • Is every relation a function? ____ • Is every function a relation? ____ • Function or not • May x go to two different y’s? ____ • May y go to two different x’s? ____ • Domain vs. Range Chart • What are the different ways to represent a relation? • What is the Vertical Line Test?

More Related