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Intro to Functions: Understanding Domain, Range, and Function Notation

Learn about functions, domains, ranges, and function notation in mathematics. Evaluate expressions and determine if they are functions. Practice with examples and understand the concepts clearly. Homework problems included.

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Intro to Functions: Understanding Domain, Range, and Function Notation

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  1. 4 minutes Warm-Up Evaluate each expression. • x – 2, for x = -5 • -2x, for x = -1.5 • x2, for x = -4 • -x2, for x = -1.2 • x3, for x = -2 • -x3, for x = -0.1

  2. 2.3 Intro 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

  3. Definition of a Function Function: each value of the first variable is paired with exactly one value of the second variable Domain: set of all possible values of the first variable Range: set of all possible values of the second variable

  4. Example 1 State whether the data in each table represents y as a function of x. Explain. function not a function

  5. Vertical-Line Test If every vertical line intersects a given graph at no more than one point, then the graph represents a function. function not a function

  6. Definition of a Relation Relation: each value of the first variable is paired with one or more values of the second variable Domain: set of all possible values of the first variable Range: set of all possible values of the second variable

  7. Example 2 State the domain and range of the relation, and state whether it is a function. { (–7, 5), (4, 12), (8, 23), (16, 8) } domain: { –7, 4, 8, 16} range: { 5, 8, 12, 23 } This is a function because each x-coordinate is paired with only one y-coordinate.

  8. Function Notation If there is a correspondence between values of the domain, x, and values of the range, y, that is a function, then y = f(x), and (x,y) can be written as (x,f(x)). The variable x is called the independent variable. The variable y, or f(x) is called the dependent variable.

  9. Example 3 Evaluate f(x) = –2.5x + 11, where x = –1. f(–1) = –2.5 (–1) + 11 f(–1) = 2.5 + 11 f(–1) = 13.5

  10. Example 4 A gift shop sells a specialty fruit and nut mix at a cost of $2.99 per pound. During the holiday season, you can buy as much of the mix as you like and have it packaged in a decorative tin that costs $4.95. a) Write a linear function to model the total cost in dollars, c, of the tin containing the fruit and nut mix as a function of the number of pounds of the mix, n. c(n) = 4.95 + 2.99n b) Find the total cost of a tin that contains 1.5 pounds of the mix. c(n) = 4.95 + 2.99n c(1.5) = 4.95 + 2.99(1.5) c(1.5) = 9.44 $9.44

  11. Homework p.107 #17-49 odds

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