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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.
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Polynomials andPolynomial Expressions
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- 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
- 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
- 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
- Sketchthe graph of a function using common graphs and transformations
- Writethe equation of function using common graphs and transformations
- 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
- 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.)
- 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
- 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
- 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
- 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
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