20804212College Algebra
Course Information
Description
This course covers skills needed for success in Calculus and many application areas at the baccalaureate level. Topics include the real and complex number systems, polynomials, exponents, radicals, solving equations and inequalities, relations and functions, systems of equations and inequalities, graphing, and conic sections.
Total Credits
3
Course Competencies
  1. Analyze the features of a graph of a given function or relation
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    graph a relation or function in x and y
    differentiate between symmetry about the x-axis, the y-axis, and the origin
    determine the domain and range of a relation or function
    define a 1-1 function
    apply the horizontal line test for a 1-1 function
    determine the inverse function of a 1-1 function
    specify the relation between the domain and the range of a function and its inverse
    apply basic transformations to the elementary functions
    differentiate among elementary functions

  2. Solve linear and quadratic equations and inequalities
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    relate the solution of an equation to the x-intercept of a graph of the function and to the root (or zero) of the function
    solve linear equations and inequalities
    use appropriate notations when writing solutions of inequalities
    solve quadratic equations using more than one method
    use modeling techniques to solve applied problems

  3. Analyze the properties of linear and quadratic functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    graph quadratic functions
    apply multiple transformations to quadratic functions
    determine the composition of two functions
    create new functions by using function operations
    note when function composition is non-commutative
    apply transformations as compositions of functions
    determine the characteristics of a quadratic function
    find zeros of quadratic functions algebraically and graphically
    convert between standard and graphing form of a quadratic function

  4. Analyze polynomials
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    find zeros of polynomial functions
    determine whether a function is increasing or decreasing on an interval
    determine the behavior of a polynomial function at the end points of its domain
    use graphical methods to estimate the roots of a polynomial equation
    identify local and global extrema
    apply the intermediate value theorem
    use the fundamental theorem of algebra to determine the number of roots of a polynomial equation
    use the fundamental theorem of algebra to determine the number of roots of a polynomial function
    identify the degree of a polynomial function
    determine all solutions to polynomial equations including complex solutions

  5. Analyze rational functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    simplify complex fractions
    identify removable discontinuities
    graph rational functions
    perform arithmetic operations with rational expressions
    determine the domain of rational functions
    determine all asymptotes
    solve rational equations
    solve rational inequalities (optional)

  6. Analyze radical functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    solve radical equations
    graph radical functions
    verify solutions to identify extraneous roots
    determine the domain of radical expressions

  7. Analyze exponential and logarithmic functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    define exponential functions with an arbitrary base
    graph an exponential function with an arbitrary base
    model exponential functions to real life applications
    solve exponential equations
    define logarithmic functions with an arbitrary base
    identify the inverse relationship between the logarithmic function and the exponential function
    graph a logarithmic function with an arbitrary base
    solve logarithmic equations
    determine the domain and range of logarithmic functions

  8. Solve algebraic systems
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    solve nonlinear systems of equations
    solve systems of linear equations in three or more variables
    use systems of three equations to solve applied problems
    graph systems of linear inequalities
    graph systems of nonlinear equations
    solve systems of equations using matrices (optional)
    introduce partial fraction decomposition (optional)

  9. Analyze conic sections
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    identify all conic sections based on a graph
    identify all conic sections based on an equation
    analyze the characteristics of all conic sections
    sketch the graph of all conic sections given their equations

  10. Analyze series and sequences (optional)
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    find terms of sequences given the nth term
    convert between sigma notation and other notation for a series
    find the nth term of an arithmetic and geometric sequence
    find the common ratio of a geometric sequence