By Raymond A. Barnett
Mathematical reform is the driver at the back of the association and improvement of this new collage algebra textual content. using know-how, basically graphing utilities, is thought in the course of the textual content. the improvement of every subject proceeds from the concrete to the summary and takes complete benefit of expertise, anywhere applicable. the 1st significant target of this ebook is to inspire scholars to enquire mathematical rules and approaches graphically and numerically, in addition to algebraically. continuing during this method, scholars achieve a broader, deeper, and extra beneficial knowing of an idea or approach. even if suggestion improvement and expertise are emphasised, manipulative talents will not be neglected, and lots of possibilities to perform easy talents are current. a quick examine the desk of contents will demonstrate the significance of the functionality thought as a unifying subject matter. the second one significant target of this ebook is the improvement of a library of effortless features, together with their vital homes and makes use of. Having this library of uncomplicated services as a simple operating software of their mathematical device packing containers, scholars should be capable of stream into calculus with higher self belief and figuring out. furthermore, a concise evaluate of uncomplicated algebraic suggestions is incorporated in Appendix A for simple reference, or systematic evaluation. The 3rd significant goal of this ebook is to offer the scholar enormous event in fixing and modeling actual global difficulties. sufficient functions are incorporated to persuade even the main skeptical scholar that arithmetic is basically worthy. many of the purposes are simplified models of exact real-world difficulties taken from specialist journals books. No really expert event is needed to resolve any of the purposes.
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Additional resources for College Algebra: Graphs & Models, 3rd Edition
Qxd 11/22/2007 06:15 PM Page 37 pinnacle 110:MHIA064:mhbar3:SE:CH 01: S E C T I O N 1–2 EXAMPLE Functions 37 Evaluating and Simplifying a Difference Quotient 9 * For f (x) ϭ x2 ϩ 4x ϩ 5, find and simplify: (A) f (2) (B) f (2 ϩ h) (D) f (x ϩ h) (E) (C) f (x ϩ h) Ϫ f (x) h f (2 ϩ h) Ϫ f (2) h SOLUTIONS (A) f (2) ϭ 22 ϩ 4(2) ϩ 5 ϭ 17 (B) To find f (2 ϩ h), replace x with 2 ϩ h everywhere it occurs in the equation that defines f, then simplify: f (2 ؉ h) ϭ (2 ؉ h)2 ϩ 4(2 ؉ h) ϩ 5 ϭ 4 ϩ 4h ϩ h2 ϩ 8 ϩ 4h ϩ 5 ϭ h2 ϩ 8h ϩ 17 (C) Using parts (A) and (B), we have f(2 ϩ h) f(2) f (2 ϩ h) Ϫ f (2) (h2 ϩ 8h ϩ 17) Ϫ (17) ϭ h h ϭ h(h ϩ 8) h2 ϩ 8h ϭ ϭhϩ8 h h (D) To find f (x ϩ h), we replace x with x ϩ h everywhere it appears in the equation that defines f and simplify: f (x ؉ h) ϭ (x ؉ h)2 ϩ 4(x ؉ h) ϩ 5 ϭ x2 ϩ 2xh ϩ h2 ϩ 4x ϩ 4h ϩ 5 (E) Using the result of part (D), we get f(x ϩ h) f(x) f (x ϩ h) Ϫ f (x) (x ϩ 2xh ϩ h ϩ 4x ϩ 4h ϩ 5) Ϫ (x ϩ 4x ϩ 5) ϭ h h x2 ϩ 2xh ϩ h2 ϩ 4x ϩ 4h ϩ 5 Ϫ x2 Ϫ 4x Ϫ 5 ϭ h 2 ϭ 2 2xh ϩ h2 ϩ 4h h MATCHED PROBLEM 2 ϭ h(2x ϩ h ϩ 4) h 9 Repeat Example 9 for f (x) ϭ x2 ϩ 3x ϩ 7.
True or False: Every relation is a function. Explain your answer. 2. True or False: Every function is a relation. Explain your answer. 3. Explain the difference between f (x ϩ h) and f (x) ϩ h. 4. Explain the difference between f (x), where f represents a function, and 2(x). Indicate whether each relation in Problems 5–10 defines a function, then write each as a set of ordered pairs. 5. Domain Range 6. Domain 12. 5(Ϫ1, 4), (0, 3), (1, 2), (2, 1)6 13. 5(10, Ϫ10), (5, Ϫ5), (0, 0), (5, 5), (10, 10)6 14.
Round answers to two decimal places. (Hint: See Exercises 31–40) 40. 1x ϩ 5x 2 41. * (B) Graph y1 ϭ 29 Ϫ x2 and y2 ϭ Ϫ 29 Ϫ x2 in the standard viewing window of a graphing calculator. How do these graphs compare to the graph you drew in part A? (C) Apply each of the following ZOOM options to the graphs in part B and determine which options produce a curve that looks like the curve you drew in part A: ZDecimal, ZSquare, ZoomFit 51. 2 x4 ϩ x3 ϭ 1 xϩ2 2 52. 1x ϩ 9 ϩ 3 ϭ 9 ϩ x Ϫ 5x2 53. x2 Ϫ 3x ϩ 1 ϭ 12x Ϫ 7 3 2 54.