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2.3 – Introduction to Functions. Objectives: State the domain and range of a relation, and tell whether it is a function. Write a function in function notation and evaluate it. Standards: 2.8.11.S. Analyze properties and relationships of functions.
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2.3 – Introduction to Functions • Objectives: • State the domain and range of a relation, and tell whether it is a function. • Write a function in function notation and evaluate it. • Standards: • 2.8.11.S. Analyze properties and relationships of functions. • 2.8.11.O. Determine the domain and range of a relation.
Warm Up: - 7 3 16 - 1.44 - 8 0.001
The domain of a function is the set of all possible values of x (the inputs). • The range of a function is the set of all possible values of y (the outputs).
Examples: State whether the data in each table represents a function. a). b). a). b).
More Examples: Ex. 1d Ex. 1c NO YES
c). d). Not a function. It does not pass the vertical line test. Not a function. It does not pass the vertical line test.
The domain of a function is the set of all possible values of x (the inputs). • The range of a function is the set of all possible values of y (the outputs). Domain: {-2, 0, 3, 8} Range: {-26, -6, 24, 74} Domain: {-6, -4, 2, 3} Range: {7, 12, 19, 39}
III. A function is a special type of relation. A relationship between two variables such that each value of the first variable is paired with one or more values of the second variable is called a relation. Ex 4. b. D: R:
State the domain and range of eachgraphed. c. d. Open circle D: x > -2 R: y > -1
Functions and Function Notation y = 2x + 5 → f (x) = 2x + 5 If there is a correspondence between the domain and range that is a function, then y = f(x), and (x, y) can be written as (x, f(x)). The number represented by f(x) is the value of the function f at x. The variable x is called theindependent variable. The variable y, or f(x), is called thedependent variable.
