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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 .

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Relations

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  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?

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