College Algebra & Trigonometry, 2018a

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Chapter 4 Functions A function is generally defined as a relation in which each x value corresponds to one and only one y value. This assigning of only one y value to each x is known as “univalence.” The univalence requirement makes some manipulations in calculus easier to work with and can be important in certain applications, but many important relations (such as the hyperbola, circle and ellipse) are not univalent and thus not functions. A function typically describes a relationship between two sets. In our consideration of functions these two sets will typically be real or complex numbers. Functions are usually defined in one of several ways. They can be defined by (1) a graph, (2) an algebraic relationship, (3) a rule or (4) a table of values. More than one of these methods can be used to describe the same function. 4.1 Function Notation The notation for a function is generally the f(x) notation. In learning about graphing in algebra we typically use the x and y notation, that is: y =6x − 1. In function notation, the dependent variable y is replaced by the notation f(x) : f(x) =6x − 1 Function values for particular values of the independent variable x can be found 189
190 CHAPTER 4. FUNCTIONS by substituting the appropriate x value into the formula. f(9) = 6(9) − 1=53 f(9) = 53
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College Algebra & Trigonometry
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c○2018 Richard W. Beveridge This
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4 CONTENTS 2.4 Solution of Rational
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6 CONTENTS 8.2 The Trigonometric Ra
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8 CONTENTS
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10 CHAPTER 1. ALGEBRA REVIEW Exampl
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12 CHAPTER 1. ALGEBRA REVIEW 2(x +3
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30 CHAPTER 1. ALGEBRA REVIEW Then,
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40 CHAPTER 1. ALGEBRA REVIEW devise
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44 CHAPTER 1. ALGEBRA REVIEW Exerci
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74 CHAPTER 1. ALGEBRA REVIEW Exampl
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80 CHAPTER 1. ALGEBRA REVIEW Addend
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84 CHAPTER 1. ALGEBRA REVIEW 26) On
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86 CHAPTER 1. ALGEBRA REVIEW 40) A
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88 CHAPTER 2. POLYNOMIAL AND RATION
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100 CHAPTER 2. POLYNOMIAL AND RATIO
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240 CHAPTER 4. FUNCTIONS Exercises
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242 CHAPTER 4. FUNCTIONS 8) A recta
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244 CHAPTER 4. FUNCTIONS So, our fi
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246 CHAPTER 4. FUNCTIONS Exercises
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248 CHAPTER 4. FUNCTIONS Distance O
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250 CHAPTER 4. FUNCTIONS The graph
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252 CHAPTER 4. FUNCTIONS Distance/T
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254 CHAPTER 4. FUNCTIONS The graph
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256 CHAPTER 4. FUNCTIONS 3) A power
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258 CHAPTER 5. CONIC SECTIONS - CIR
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288 CHAPTER 6. SEQUENCES AND SERIES
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306 CHAPTER 7. COMBINATORICS differ
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308 CHAPTER 7. COMBINATORICS Exampl
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322 CHAPTER 7. COMBINATORICS SET II
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344 CHAPTER 8. RIGHT TRIANGLE TRIGO
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384 CHAPTER 9. GRAPHING THE TRIGONO
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438 CHAPTER 10. TRIGONOMETRIC IDENT
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472 CHAPTER 11. THE LAW OF SINES TH
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College Algebra & Trigonometry, 2018a

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