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Functions

Functions. Objective: To identify functions and find the domain and range of relations and functions. Standard(s): F.IF.1. Bell Work. Generate ordered pairs for the function y = x + 3. For x = -2, -1, 0, 1, and 2. Graph the ordered pairs. (-2, 1) (-1, 2) (0, 3) (1, 4) (2, 5).

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Functions

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  1. Functions Objective: To identify functions and find the domain and range of relations and functions. Standard(s): F.IF.1

  2. Bell Work Generate ordered pairs for the function y = x + 3. For x = -2, -1, 0, 1, and 2. Graph the ordered pairs. (-2, 1) (-1, 2) (0, 3) (1, 4) (2, 5)

  3. Function • A function is a special type of relation that pairs each domain value to exactly one range value. • A relation is a set of ordered pairs of the form (x, y). • The equation y = x + 4 describes a relation. It relates the value of y to the value of x.

  4. Representing Relation A relation can be represented as: Equation y = 6x-2 Table A list of ordered pairs {(1, 3), (2, 4), (3, 5)} Graph Mapping Diagram

  5. Graphical Representation • Some graphs are connected by lines or curves called continuous graphs. • Some graphs are only distinct points. These are called discrete graphs. Usually used to display whole number data. Discrete Graph Continuous Graph

  6. Showing Multiple Representations of Relations Express the relation for the track meet scoring system, {(1, 5) , (2, 3) , (3, 2) , (4, 1)}, as a table, as a graph, and as a mapping diagram.

  7. Function Notation • A function can be written as an equation using function notation f(x). • f(x) is read as “f of x”. • f(x) takes the place of y and stands for the output of the function for the input of x.

  8. Function Notation Evaluate f(x)=2x + 1 for x = 2

  9. Domain and Range • The set of all possible input values (x) for a function is called the function’s domain. • The set of all possible outputs (y) for a function is called the range. • The domain and range are sets that consists of values called an element.

  10. A function relates each element of a set with exactly one element of another set (possibly the same set). • Note: "One-to-many" is not allowed, but "many-to-one" is allowed. (one-to-many) This is NOT OK in a function (many-to-one) But this is OK in a function

  11. Give the domain and range of the relation.

  12. Give the domain and range of the relation.

  13. Give the domain and range of the relation.

  14. Identifying Functions Give the domain and range of each relation. Tell whether the relation is a function. Explain.

  15. Identifying Functions Give the domain and range of each relation. Tell whether the relation is a function. Explain.

  16. Identifying Functions Give the domain and range of each relation. Tell whether the relation is a function. Explain.

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