May 28th, 2015
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ADVANCED ALGEBRAUnfinishedMathematical Relations and FunctionsFunctions- A relation wherein the elements of the first set is related to exactly one of the second group. (In other words, its like monogamy except your life partner could be cheating on you.)Domains and ranges:Domain- the x or the first group (the monogamist/you)Ranges- the y or second group (the possible polygamist/your life partner)Operations involving functionsSUM OF F AND G: (f+g)(x) = f(x) + g(x)DIFFERENCE OF F AND G: (f-g)(x) = f(x) g(x)PRODUCT OF F AND G: (f x g)(x) = f(x) x g(x)QUOTIENT OF F AND G: (f/g)(x) = f(x)/g(x), g(x) is not equal to zero (or else itll be undefined. I think.)COMPOSITE OF F AND G: (f o g)(x) = f(g(x))Polynomial FunctionsDefinition f(x) = AnXn + An-1Xn-1.AnX2 + A1X + AWhere n is a positive integer, is not equal to zero,And An, A,n-1, . A2, , A1 and A are REAL MONSTERS NUMBERS.Form (General and Standard) and Examples 1. Linear: f(x) = mx + b; m is not equal to 02. Quadratic: f(x)= ax2+ bx + c, a is not equal to 0 (itll cancel out the x squared, making it linear. Pointless.)3. Cubic: f(x) = ax3 + bx2 +cx + d, a is not equal to 0 (same reason above)Domain, range, rule and graphsLINEAR:Formulaf(x) = mx + b, where m is not equal to 0Slope (steepness of the line)Given two points (x1, y1) and (x2, y2).Slope = y2-y1/x2-x1 Slope = rise/runSlope= vertical change/ horizontal changeY-Intercept (point found on the

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