Chapter 1-4Quadratics, Functions, Exponentials, Logarithms



right494450Chapter 1 | Quadraticsright1211293Ways to Solve Quadratic EquationsFactorize and use the Null Factor LawComplete the squareUse the quadratic formulaUse technology4000020000Ways to Solve Quadratic EquationsFactorize and use the Null Factor LawComplete the squareUse the quadratic formulaUse technologyleft116285300Quadratic Formulaleft65437300Completing the Squareright1686572The DiscriminantComponents of the Equationcenter94866right295143Things to Know about an EquationOptimizationUsing knowledge of the axis of symmetry, which is also the vertex, in a quadratic equation.center5561600Chapter 2 | Functionsright571500Relation – any set of points which connect two variablesHowever a relation may not be able to be defined by an equationFunction – a relation in which no two different ordered pairs have the same x-coordinate Testing for FunctionsAlgebraic TestSubstitute a value for x and if you only get one y-value, it’s a functionVertical Line Test/Geometric TestDraw vertical linesIf each line cuts the graph at most once, it’s a functionComposite FunctionsIn general, (f°g)(x) is not the same as (g°f)(x)Inverse FunctionsIf (x, y) lies on f, then (y, x) lies on f-1Must satisfy the vertical line testIs the reflection of y=f(x) in the line y=xSatisfies (f°f-1)(x) = x and (f-1°f)(x) = xHorizontal line test – for a function to have an inverse, no horizontal line can cut its graph more than onceIdentity function – returns the same valuey = xSelf-inverse function – function that has an inverse equal to itself (and is symmetrical about line y = x)Chapter 3 | Exponentials4088765520700408892131611860Exponential EquationsWhen the unknown occurs in the exponentIf the bases are the same, EQUATE the exponentsExponential FunctionsWe can sketch graphs of exponential functions using:The horizontal asymptoteY-interceptleft24701500Two other pointsChapter 4 | LogarithmsLogarithms – the inverse of the exponential functionright3067050left3162300Rules of Logarithmscenter1491615right236855Logarithm EquationsExponential Equations and their Inverse (Logarithmic Equations)right33337500left6667500 ................
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