College Algebra & Trigonometry, 2018a

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4.1. FUNCTION NOTATION 191 Exercises 4.1 Find each of the following values for the given functions: f(0) f(−1) f(3) f( 1 ) f(x +2) f(x + h) 2 1) f(x) =2x 2 − 3x +1 2) f(x) =5x 2 + x − 7 3) f(x) = x x 2 − 1 4) f(x) = x +3 x 2 +1
192 CHAPTER 4. FUNCTIONS 4.2 Domain and Range of a Function The analysis of the behavior of functions addresses questions of when the function is increasing or decreasing, whether and where it has maximum or minimum values, where it crosses the x or y axis, and which values of x and y aretobeincluded in the function. The set of values available for the x, or independent variable is called the Domain of the function. The set of corresponding y values is called the Range of the function. The linear function mentioned above f(x) = 6x − 1 has a domain of all real numbers and a range of all real numbers, x ∈ R and y ∈ R . On the other hand, the function f(x) =x 2 has a domain of all real numbers, x ∈ R, but its range is limited to the positive real numbers, y ≥ 0. Considerations of the domain of a function typically refer to restrictions on which x values will generate real number values for y. The most common restrictions occur with the use of square root functions or rational functions. The domain of the function f(x) = √ x − 7 would be the set of x ≥ 7, so that no negative values are permitted under the square root. This secures the necessary real values for y. The range for this function is y ≥ 0. x The domain of the function f(x) = would be x ∈ R (all real numbers), 2x − 3 but x ≠ 3 , thus avoiding a zero denominator which is an undefined value. The 2 range for this function would be y ∈ R (all real numbers), but y ≠ 1 , due to the 2 horizontal asymptote at y = 1. 2 The questions of domain and range become more interesting when considered in relation to functions defined by graphs, or in applications. In an application involving perimeter in which the perimeter of a rectangle is given as 50 feet, we know that 2l +2w =50 Rewriting this as a function of w, we can say that l = f(w) =25− w
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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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88 CHAPTER 2. POLYNOMIAL AND RATION
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288 CHAPTER 6. SEQUENCES AND SERIES
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College Algebra & Trigonometry, 2018a

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