By Ross L. Finney, Franklin D. Demana, Bert K. Waits, Daniel Kennedy
The major target of this 3rd variation is to realign with the alterations within the complicated Placement (AP ) calculus syllabus and the hot form of AP examination questions. now we have additionally extra conscientiously aligned examples and routines and up-to-date the knowledge utilized in examples and workouts. Cumulative fast Quizzes are actually supplied or thrice in every one chapter.
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Additional info for Calculus: Graphical, Numerical, Algebraic
Note that the first equation will cause x to take on all real values, because x2 – x1 is not zero. Therefore, all of the points on the line will be traced out. (b) Use the equations for x and y given in part (a) with 0 Յ t Յ1. 5 What you’ll learn about • One-to-One Functions • Inverses • Finding Inverses • Logarithmic Functions • Properties of Logarithms 37 Functions and Logarithms One-to-One Functions As you know, a function is a rule that assigns a single value in its range to each point in its domain.
Y ϭ e x ϩ 3 3. y ϭ 3 • eϪx Ϫ 2 Domain: All reals Range: (Ϫ2, ϱ) 4. 9 Range: (Ϫϱ, Ϫ1) In Exercises 5–8, rewrite the exponential expression to have the indicated base. 5. 92x, 7. 6. 163x, base 3 34 x (1͞8)2x, base 2 2Ϫ6x 8. base 2 212x (1͞27) x, base 3 3Ϫ3x In Exercises 9–12, use a graph to find the zeros of the function. 9. 322 11. 631 19. 9 gives the population of Nevada for several years. 10. 386 12. 585 Population of Nevada Year Population (thousands) 1998 1999 2000 2001 2002 2003 1,853 1,935 1,998 2,095 2,167 2,241 Source: Statistical Abstract of the United States, 2004–2005.
Y ϭ 2 ln (3 Ϫ x) Ϫ 4 40. y ϭ Ϫ3 log (x ϩ 2) ϩ 1 41. y ϭ log2 (x ϩ 1) 42. y ϭ log3 (x Ϫ 4) Domain: (Ϫ1, ϱ); Range: all reals No y = 1x 100 50 44. f (x) ϭ ᎏᎏ 43. 1Ϫx 45. Self-inverse Prove that the function f is its own inverse. Ϫෆ x 2ෆ, (a) f (x) ϭ ͙1ෆෆ 6. Yes No y = –3x3 x xՆ0 (b) f (x) ϭ 1͞x 46. Radioactive Decay The half-life of a certain radioactive substance is 12 hours. There are 8 grams present initially. y y = int x (a) Express the amount of substance remaining as a function of t/12 time t.