tailieunhanh - College Algebra

For many students a College Algebra course represents the first opportunity to discover the beauty and practical power of mathematics. Thus instructors are faced with the challenge of teaching the concepts and skills of algebra while at the same time imparting a sense of its utility in the real world. In this edition, as in the previous four editions, our aim is to provide instructors and students with tools they can use to meet this challenge. The emphasis is on understanding concepts. Certainly all instructors are committed to encouraging conceptual understanding. For many this is implemented through the rule of four: “Topics should be presented geometrically, numerically,. | COLLEGE ALGEBRA I 5e JAMES STEWART I LOTHAR REDLIN I SALEEM WATSON EXPONENTS AND RADICALS DISTANCE AND MIDPOINT FORMULAS xmx xm n xm .m-n . x xn Distance between P1 x1 y1 and P2 x2 y2 x m n x m n xy n xnyn x 1n 1x x x ixy ix iy wx. 2 x mix x n a x bn m n x 1 x n xn y n m SPECIAL PRODUCTS d V x2 - xi 2 y2 - y1 2 Midpoint of P1P2 ax1 x2 y1 y2 b 2 2 LINES jx _ 1x B y iy x y x y x2 y2 x y 2 x2 2 xy y2 x y 2 x2 2 xy y2 x y 3 x3 3x 2y 3xy2 y3 x - y 3 x3 - 3x2y 3xy2 - y3 Slope of line through P1 x1 y1 and P2 x2 y2 y2 - y1 m x2 - x1 Point-slope equation of line through P1 x1 y1 with slope m y y1 m x x1 Slope-intercept equation of line with slope m and y-intercept b y mx b Two-intercept equation of line x y 1 with x-intercept a and y-intercept b ab FACTORING FORMULAS x2 y2 x y x y x2 2 xy y2 x y 2 x2 2 xy y2 x y 2 x3 y3 x y x2 - xy y2 x3 - y3 x - y x2 xy y2 QUADRATIC FORMULA If ax2 bx c 0 then b 2b2 4ac x ----------------- 2a The lines y m 1x b1 and y m 2x b2 are Parallel if the slopes are the same m 1 m 2 Perpendicular if the slopes are m 1 1 m 2 negative reciprocals LOGARITHMS y logax means ay x logaax x alogax x loga 1 0 logaa 1 Common and natural logarithms log x log10 x ln x logex Laws of logarithms logaxy logax logay INEQUALITIES AND ABSOLUTE VALUE If a b and b c then a c. If a b then a c b c. If a b and c 0 then ca cb. If a b and c 0 then ca cb. If a 0 then x a means x a or x a. x a means a x a. x a means x a or x a. yb loga x - loga y logaxb b logax Change of base formula logb x log a x log a b GRAPHS OF FUNCTIONS Linear functions fix mx b f x mx b Exponential functions fix ax fX Absolute value function Greatest integer function f w lxl fW x SHIFTING OF FUNCTIONS Root functions fix 1x Vertical shifting y y x x f Tx fix ựx y f c y f yfc x c 0 Reciprocal functions fix Horizontal .