Final Exam Review Chapter 1 Exponents: xmxn= xm+n x− m=1xmxm()n= xmn xmxn= xm−nx0= 1 xy()m= xmymxy⎛ ⎝ ⎜ ⎞ ⎠ ⎟ m=xmymxab=xab Radicals: Polynomials: adding, subtracting, multiplying, dividing factoring -- look for common factors first three terms--trial and error two terms--formula or common factor Rational expressions (fractions with polynomials): adding, subtracting, multiplying, dividing Complex fractions (fraction over a fraction) Rationalizing Chapter 2 Solving equations: linear rational equations (fractions with variable in denominator)--either an answer you can use, an answer you can’t use (no solution) or all real x except x =??Applications Solving quadratic equations--ax2+bx+c=0 (1) solve by factoring (2) solve by completing the square (do not have to) (3) solve by quadratic formula x =−b± b2− 4ac2a Imaginary numbers Radical equations, absolute value equations, etc. Inequalities, absolute value inequalities: x< b x> b−b <x< b x<−b or x> b means (2) means (1) Chapter 3 distance formula: d = x2− x1()2+ y2− y1()2 midpoint formula: x1+ x22,y1+y22⎛ ⎝ ⎜ ⎞ ⎠ circles: x− h()2+ y− k()2= r2 Lines: slope = m =y2− y1x2− x1 equations of lines: (1) y− y1= mx− x1()(2) y = mx + bgeneral formFinding function values or expressions Domain, range, increasing, decreasing... Stretching, shifting, reflecting of graphs piece-wise functions Parabolas: Standard form: y = ax− h()2+ kVertex: h,k() Quadratic form: y = ax2+ bx + cVertex: x -coord = −b2a or find average of x-int. plug in to find y Add, subtract, multiply, divide two functions Composition of functions f g Inverse functions Directly proportional: y = kxInversely proportional: y =kx Solving (graphing) inequalities using a sign chart Chapter 9 Two equation/two unknowns substitution/elminationChapter 5 Exponential equation: y=ax Logarithmic equation: x=ay or y=logax Properties: 1() logauw()= logau+logaw2() logauw⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = logau− logaw3() logauc= clogau Change of base formula: logbu =logaulogab Only formulas given: A = P 1+rn⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ntA =
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