1007slides_Part1

# 1007slides_Part1 - Math 1007 Fall 2006(These slides replace...

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Unformatted text preview: Math 1007, Fall 2006 (These slides replace neither the text book nor the lectures.) Part I: Introduction 1. Lines (2) 2. Equation of a Line (3) 3. Factoring (4) 4. Functions and Their Graphs (5-6) 5. Intervals (7) 6. Algebra of Functions (8) 7. Symmetry (9) 8. Increasing and Decreasing Functions (10) 9. Catalog of Essential Functions (11-14) 10. An important Value (15) 1 1. Lines (Appendix B) The slope of a line l is defined by the quotient m = Δ y Δ x = y 2- y 1 x 2- x 1 . Horizontal lines (y=b) have slope zero and vertical lines (x=a), have undefined slope (slope is said to be ∞ ). Two lines are parallel if and only if they have the same slope. Two non-vertical lines l 1 and l 2 are perpendicular if and only if ( m 1 )( m 2 ) =- 1, where m 1 is the slope of l 1 and m 2 is the slope of l 2 . 2 2. Equation of a Line (Appendix B) Slope-intercept form of a line : Given the slope m and the y-intercept b , so that the point (0 ,b ) is on the line, the equation of the line is y = mx + b. Point-slope form of a line : Given the slope m and a point ( x 1 ,y 1 ) on the line, the equation of the line is y- y 1 = m ( x- x 1 ) . 3 3. Factoring (Reference pages) Difference of two squares x 2- y 2 = ( x + y )( x- y ) Sum of two cubes x 3 + y 3 = ( x + y )( x 2- xy + y 2 ) Difference of two cubes x 3- y 3 = ( x- y )( x 2 + xy + y 2 ) Quadratic Formula: Solutions to ax 2 + bx + c = 0 ( a 6 = 0) are x =- b ± p b 2- 4 ac 2 a Common denominator for addition of fractions a b + c d = ad + bc bd 4 4. Functions and Their Graphs (1.1)4....
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## This note was uploaded on 03/22/2010 for the course MATH 1007 taught by Professor Unknown during the Fall '07 term at Carleton.

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1007slides_Part1 - Math 1007 Fall 2006(These slides replace...

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