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ALGEBRA HOW TO FIND A AND B VALUE IN THE INTERMEDIATE VALUE THEOREM
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- Understandthe Cartesian coordinate system and the idea oflocating ordered pairs of numbers.
- Knowand use the mid-point and distance formulas to solve real worldproblems.
- Knowhow to graph relations in the coordinate plane.
- Find domainand range of a relation from a list or ordered pairs, graph or atable of values.
- Recognizeand evaluate basic features of a graph of a relation.
- Producegraphs of simple relations using tables.
- Findthe x and y-intercepts of the graph of an equation(algebraically and graphically)
- Determinethe symmetry of the graph of an equation (algebraically andgraphically)
- Writethe General Form Equation of a circle in Standard Form and determinethe center and radius of the circle
| BasicFeatures of a Graph - domainand restricted values
- range
- x and y intercepts
- intervalswhere a graph is constant, increasing or decreasing
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LinearEquations and Inequalities
- Solvelinear equations algebraically and graphically.
- Deal withfractional coefficients in equations.
- Solve equationsinvolving absolute value algebraically.
- Solve aformula for a given variable.
- Solve wordproblems by setting up and solving a linear equation in onevariable.
- Solve linearinequalities in one variable including compound inequalitiesand inequalities involving absolute value algebraically.
- Represent(graph or plot) solution sets of inequalities on the number line.
QuadraticEquations
- Solvequadratic equations by a variety of methods.
- Use thediscriminant to understand when a quadratic has no, one or two realroots algebraically.
- Solvesimple word problems using quadratic equations
- Constructand use a quadratic model to solve an application problem
| Methodsof Solving Quadratics - Byfactoring and Using Zero Factor Property when possible.
- By extracting square roots
- By completing the square
- Usingthe Quadratic formula
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Polynomials andPolynomial Expressions
- Performbasic operations with polynomials (add, subtract, multiplyincluding FOIL)
- Useformulas for these special products:
- Factorpolynomials by factoring out the Greatest Common Factor,by grouping, and by using special products formulas for trinomials
- Factorsimple trinomials of form a x^{2} + b x +c by guess-and-check or by grouping
- Solvesimple equations using the Zero Factor Propertywhen possible.
- Solvepolynomial inequalities (degree > 1)
| The Specialproducts: - (a+ b)^{2}
- (a- b)^{2}
- (a+ b)(a - b)
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SolvingNon-linear Inequalities - Use critical numbers todetermine test intervals for a polynomial inequality
- Solve a polynomialinequality algebraically and graphically
- Construct and use apolynomial inequality to solve an application problem
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Rational Expressions
- Know how todecide the domain of a rational expressions. (Decide what values areexcluded by the denominator.)
- Simplify andperform basic operations involving rational expressions (addition,subtraction, multiplication, division)
- Find a LeastCommon Denominator and use it to add or subtract rational expressions.
- Solveequations with rational expressions. Recognize that some solutions maybe extraneous and check for that.
- Within thecontext of sections covered, apply rational expressions to simplesituations.
OtherTypes of Equations and Inequalities
- Solveequations involving radicals or rational exponents
- Solveequations involving rational fractions
- Solveequations involving absolute values
- Solve higherdegree polynomial equations by factoring
- Solveequations methods as appropriate.
Equationsof the Line and Linear Inequalities
| Representationsof a line: - Standardform: A x + B y = C where A, B, and C are any realnumbers.
- Slope-interceptform: y = m x + bwhere m is the slope of a line and b is they-intercept.
- Point-slopeform: y - k = m (x - h)where (h,k) is any point on the line.
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SpecialSlope Relationships. - Horizontallines (m = 0)
- Vertical lines (m is undefined)
- Parallellines (m_{1 }= m_{2})
- Perpendicularlines (m_{1 }m_{2} = -1)
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GeneralFunction Concepts
Definitionand Notation
- Determineif an equation or a set of ordered pairs represents a function
- Usefunction notation
- Evaluatea function
- Find thedomain of a function
- Createand apply a piecewise-defined function.
- Interpretinput and output of real-life functions
- Solve anapplication problem involving real-life functions
Graphsof functions
- Finddomain and range using the graph of a function
- VerticalLine Test
- Describethe increasing and decreasing behavior of a function
- Classifya function as even or odd
- Identifysix common graphs
Transformationsof Functions
- Sketchthe graph of a function using common graphs and transformations
- Writethe equation of function using common graphs and transformations
Algebra ofFunctions
- Find thesum, difference, product, and quotient of functions
- Find thecomposition of two functions and determine the domain and range
- Identifya function as the composition of two functions
- Solvereal-life problems involving combinations and composition of functions
InverseFunctions
- Determineif a function has an inverse function (Horizontal Line Test)
- Find theInverse of a function
- Graph afunction and its Inverse (Know that the graph of f^{ -1} is areflection of the graph of f across the line y = x.)
Polynomial Functions
Polynomialdivision
- Dividepolynomials using long division
- Dividepolynomials using Synthetic division
- Use theRemainder Theorem to evaluate a polynomial
- Use theFactor Theorem to factor a polynomial
Complexnumbers (if covered by your instructor)
- Performoperations with complex numbers and write the results in standard form
- Solve aquadratic equation involving complex zeros
Polynomialanalysis
RationalFunctions
- Find thedomain of a rational function
- Find thevertical and horizontal asymptotes of the graph of a rational function
- Sketch thegraph of a rational function
- Use arational function model to solve an application problem
Exponential Functions
- Sketch thegraph of an exponential function
- Investigatebasic characteristics of an exponential function (domain,range, intercepts, increasing/decreasing behavior)
- Writeformulas of transformed exponential functions
- Use anexponential model to solve an application problem (in particular,models involving the natural exponential function)
- Use thecompound interest formula to solve finance problems
- Constructand use a model for exponential growth or exponential decay
LogarithmicFunctions
- Propertiesof logarithms
- SolveLogarithmic and Exponential Equations
- Sketch thegraph of a logarithmic function
- Investigatebasic characteristics of a logarithmic function (domain, x-intercept,vertical asymptote)
- Writeformulas of transformed logarithmic functions
- Use alogarithmic model to solve an application problem (in particular,models involving the natural logarithmic function)
Systems in twovariables
- Solve alinear system of equations
- Constructand use a linear system of equations to solve an applicationproblem
- Solvenonlinear systems
- Constructand use a nonlinear system of equations to solve anapplication problem
| Methodsof Solving Systems. - bysubstitution
- byelimination
- graphically
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