MATH 1111 – Content Standards

Title: College Algebra

  1. Understand the general definition of a function and be able to:
    • Illustrate a function verbally, graphically, with charts/tables, and with set notation
    • Determine the domain and range of a function
    • Identify where a function is increasing, decreasing or constant.
  2. Understand linear functions and be able to:
    • Identify, graph, and find equations of linear functions (including parallel and perpendicular lines).
    • Interpret the slope and y-intercept as an average rate of change and an initial amount, respectively.
    • Students will be able to interpret and apply these ideas in applied settings.
  3. Identify, understand and apply graph transformations of y = , y = , and y = |x| using:
    • Vertical and horizontal shifts
    • Vertical stretching and compressions
    • Reflections
  4. Understand, identify, graph, interpret and apply the following in applied settings
    • Quadratic functions of the form y =
      • Determine the vertex and intercepts.
    • Power functions and transformations of power functions
    • Polynomial functions where the polynomial is factorable.
      • Students will be able to describe the end behavior of polynomials and the relationship between end behavior and the degree of the polynomial.
      • Students will be able to determine intercepts of factorable polynomials exactly.
      • Students will be able to use appropriate technology to approximate x-intercepts and local extrema of polynomials.
    • Identify and graph transformations of y = 1/x and y = 1/ .
      • Students will be able to recognize and determine vertical and horizontal asymptotes, end behavior, and behavior near vertical asymptotes.
    • Piece-wise defined functions.
    • Compose two functions and determine the domain and range of the composite function.
    • Inverse functions
      • Get a rule for an inverse function
      • Graph a function and its inverse
    • Exponential functions of the form y = and their transformations.
    • Logarithmic functions
      • Define a logarithm
      • Convert between logarithmic and exponential forms
      • Understand the inverse relationship between logarithmic and exponential functions
  5. Determine, both algebraically and graphically, solutions to the following types of equations and apply these solutions to concepts related to functions and other applications:
    • Linear
    • Quadratic
    • Factorable polynomial
    • Rational
    • Radical (involving more than one radical)
    • Equations of the form
    • Simple exponential equations
    • Logarithmic equations using properties of logarithms.
  6. Use graphical and algebraic techniques to find solutions to the following kinds of inequalities and apply these solutions to concepts related to functions and other applications:
    • Linear
    • Quadratic
    • Factorable Polynomial
    • Rational
    • Exponential
  7. Solve linear systems of two equations in two unknowns using
    • Elimination
    • Substitution
    • Matrices
      as well as use linear systems to solve application problems.
  8. Solve simple non-linear systems of equations algebraically and graphically.