math 136: PreCalculus (3)

Course Prerequisites/Corequisites: MATH 133 (College Algebra) or by department consent.

Course Description: Designed to prepare students for the study of Calculus Sequence. Elementary functions that are differentiated and integrated in calculus stressed, including polynomial, rational, algebraic, exponential, logarithmic, and trigonometric functions. Three hours of lecture per week. Listed as MATH 2312 in the Texas Common Course Numbering System.

Textbook: Algebra and Trigonometry 10th Edition by Sullivan.

Course topics

  1. Functions and Their Graphs:
    • Function (definition, function values, domain, sum, difference, product and quotient of functions)
    • The graph of a function
      (Identify the graph of a function, obtain information from a graph)
    • Properties of functions
      (Even and odd, increasing and decreasing, maxima/minima, Average rate of change)
    • Library of functions; Piecewise-defined functions
    • Graphing techniques: Transformation
    • Mathematical Models: Building functions
  2. Polynomial and Rational Functions:
    • Polynomial functions and models
      (Definition, degree, Graph, properties of the graph of a polynomial function)
    • Properties of rational functions
      (Domain, Vertical, horizontal, oblique asymptotes)
    • The graph of rational function
      (Analyze the graph of a rational function. Solve applied problems involving rational functions)
    • Polynomial and rational inequalities
    • The real zeros of a polynomial function
    • Complex zeros: Fundamental theorem of algebra.
  3. Exponential and Logarithmic Functions
    • Composite function
    • One-to-one Functions; Inverse functions
    • Exponential functions
    • Logarithmic functions
    • Properties of Logarithms
    • Logarithmic and exponential equations
  4. Trigonometric Functions
    • Trigonometric functions: unit circle approach
      Properties of trigonometric functions
    • Graph of Sin and Cosine
    • Graph of tangent, cotangent, cosecant, and secant functions
    • Angle and their measure
    • Right Triangle Trigonometry
    • Computing the values of trigonometric functions of acute angle
    • Trigonometric function of any angle
  5. Analytic Trigonometry
    • The inverse sine, Cosine, and tangent functions
    • The inverse trigonometric functions
    • Trigonometric equations
    • Trigonometric identities
    • Sum and difference Formulas
    • Double-angle and half-angle formulas
  6. Applications of Trigonometric Functions
    • Applications involving Right triangle
    • The law of Sines
    • The law of Cosines