1 Section 2.1 Functions

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3 A relation is a correspondence between two sets. If x and y are two elements in these sets and if a relation exists between x and y, then we say that x corresponds to y or that y depends on x, and we write x  y.

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5 FUNCTION

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10 Determine whether each relation represents a function. If it is a function, state the domain and range. {(-2, 3), (4, 1), (3, -2), (2, -1)} {(2, 3), (4, 3), (3, 3), (2, -1)} {(2, 3), (4, 1), (3, -2), (2, -1)}

11 Determine if the equation defines y as a function of x.

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14 FUNCTION MACHINE

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19 (a) For each x in the domain of f, there is exactly one image f(x) in the range; however, an element in the range can result from more than one x in the domain. (b) f is the symbol that we use to denote the function. It is symbolic of the equation that we use to get from an x in the domain to f(x) in the range. (c) If y = f(x), then x is called the independent variable or argument of f, and y is called the dependent variable or the value of f at x. Summary Important Facts About Functions

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22 A rectangular garden has a perimeter of 100 feet. Express the area A of the garden as a function of the width w. Find the domain. w A A(w) = w(w-50) Domain: 0 < w < 50

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28 A)function B)not a function

29 A) B) C) D)

30 Section 2.2 The Graph of a Function

31 Average Price of Gasoline in California, Adjusted for Inflation.

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35 Which of the following are graphs of functions?

36 Which of the following are graphs of functions?

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43 A)yes, a function B)no, not a function

44 A) B) C) D)

45 Section 2.3 Properties of Functions

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47 For an even function, for every point (x, y) on the graph, the point (-x, y) is also on the graph.

48 So for an odd function, for every point (x, y) on the graph, the point (-x, -y) is also on the graph.

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50 Determine whether each graph given is an even function, an odd function, or a function that is neither even nor odd.

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53 I N C R E A S I N G D E C R E A S I N G C O N S T A N T

54 Where is the function increasing?

55 Where is the function decreasing?

56 Where is the function constant?

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75 A)even B)odd C)neither Is the function shown below even, odd or neither?

76 A)increasing B)decreasing C)constant Is the function below increasing, decreasing or constant on the interval (0, 1)?

77 Section 2.4 Library of Functions; Piecewise-defined Functions

78 The Square Root Function

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80 The Cube Root Function

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82 The Absolute Value Function

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94 WISE FUNCTIONS

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97 A)square root function B)square function C)cube function D)cube root function The graph shown below is a:

98 Which is the correct graph for the function below? A)B) C) D)

99 Section 2.5 Graphing Techniques; Transformations

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124 A) B) C) D) What is the equation for the function show below?

125 Which graph below is the graph of the function A)B) C) D)

126 Section 2.6 Mathematical Models: Building Functions

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134 A) B) C) D) Bob wants to fence in a rectangular garden in his yard. He has 62 feet of fencing to work with and wants to use it all. If the garden is to be x feet wide, express the area of the garden as a function of x.

135 Section 5.1 Composite Functions

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137 Suppose that an oil tanker is leaking oil and we want to be able to determine the area of the circular oil patch around the ship. It is determined that the oil is leaking from the tanker in such a way that the radius of the circular oil patch around the ship is increasing at a rate of 3 feet per minute.

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147 A) B) C) D)

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149 Section 5.2 One-to-One Functions; Inverse Functions

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156 For each function, use the graph to determine whether the function is one-to-one.

157 A function that is increasing on an interval I is a one-to-one function in I. A function that is decreasing on an interval I is a one-to-one function on I.

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180 A) Yes B) No Is the function shown below a one-to-one function?

181 Which of the following is the graph of the function below and its inverse? A)B) C) D)