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Unit 1Functions &AbsoluteValueSolving Abs val= and Graph and shift Abs ValAbs Val toleranceDomain & Range of FunctionsComp of functionsF(g(x))Linear regressionUnit 2QuadraticsSolving by factoring or graphGraph and shift QuadFunctionsFactoringIncludingX-Box QuadraticFormulaWordprobZeros, Max and MinDifference of squaresUnit 3 PolynomialSolving by PolynomialdivisionGraph and shift CubicFunctions

End behavx+Odd /evenRelative max and minIdentify degree of functionSimplify by factor treeAddingCombine likeMult radicalsRationalizing denomSolvingRad EquationsWorking with imag#sUnit 5 RationalsSimplifyMultDividingAddingUse LCDGraphSolve and WorkprobUnit 6 logs, exp and TrigLog to exp form and backSolving by changing formCondense and expandGrowth decay and interestTrig finding a side or angle or sin/cos/tan Unit circle

Sneak previewTo solve an absolute value equation first isolate the absolute value expression like you would a variable

Multi-Step Absolute Value Equations

Steps: 1) Isolate the absolute value 2) Rewrite as 2 equations +1 +13 I x + 2 I = 9/3 /3

x + 2 = 3 x+2 = -3 x = 1 x = -5

Absolute Value Inequalities

when you make it negative

A Model ApplicationWrite an absolute value inequality to represent this situationWhen you set your oven to 350 it is within 5 of that temperature.

When you transform a functionInside the parentheses translates left and right (opposite of what you think)Outside the parentheses translates up and down (exactly what you think)

Use the functions to evaluate the following.

xyxyDoes the graph represent a function? YESD:all realsR:y>0

NoD:all realsR:all reals

Do the ordered pairs represent a function?{(3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3, 3)}No, 3 is repeated in the domain.

{(4, 1), (5, 2), (8, 2), (9, 8)}Yes, no x-coordinate is repeated.

1x2 + 7x + 6 (x + 6)(x + 1) 2x2 - 2x 8 (x +-4)(x + 2) 3x2 + 8x + 12 (x + 6)(x + 2) 4x2 + x 20 (x + 5)(x -4) 5x2 - 8x + 15 (x - 3)(x -5)

Factor the x-box wayExample: Factor 3x2 -13x -10

-13x(3)(-10)=-30x2-15x2x-10-15x2x3x2x-53x+23x2 -13x -10 = (x-5)(3x+2)

POLYNOMIALS DIVIDINGEX Long division

(4x -15x +11x -6) / (x-3)4x - 15x + 11x - 6x - 34x4x - 12x-()-3x+ 11x- 3x-3x + 9x-()2x - 62x - 6-()+ 20R 0

Example: oddA function is odd if the degree which is greatest is odd and even if the degree which is greatest is even

Example: even

18 Using the Leading Coefficient to Describe End Behavior: Degree is EVEN

If the degree of the polynomial is even and the leading coefficient is positive, both ends ______________.

If the degree of the polynomial is even and the leading coefficient is negative, both ends ________________.

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MAT 204 SPRING 200919 Using the Leading Coefficient to Describe End Behavior: Degree is ODD

If the degree of the polynomial is odd and the leading coefficient is positive, the graph falls to the __________ and rises to the ______________.

If the degree of the polynomial is odd and the leading coefficient is negative, the graph rises to the _________ and falls to the _______________.

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MAT 204 SPRING 2009THINK(x-2) is the length of this side what binomial represents the other side Quadratic EquationQuadratic Formula

You can do things you think you cant do

#8 Simplify

Simplify

=

27#2 Solve

Standard Form

Example

What to doThenSimplifyingFactor and cancel what is in numerator and denominatorYou are doneMultiplyingFactor and cancel what is in numerator and denominator

Multiply acrossDividing1.Mult by reciprocal( flip fraction on right)2.Factor and cancel what is in numerator and denominator3. Multiply acrossAdding and subtracting1.Factor if possible.2.Make denominators common3. Add or subtract across distribute negative when subtracting

logbx = n means bn = x. Log form...exponential form23 = 8. log28=3

Growth Decay