Pre-Calculus Unit 4: Functions and Their Properties

  1. Types of Functions:

    • Polynomial Functions: Defined by polynomials; characterized by degree and leading coefficient.

    • Rational Functions: Ratio of two polynomials; essential to identify asymptotes.

    • Exponential Functions: Growth/decay; characterized by the base.

    • Logarithmic Functions: Inverse of exponential functions; understand properties of logarithms.

  2. Transformations of Functions:

    • Shifts: Horizontal and vertical shifts based on equations.

    • Reflections: Across axes; changes in signs affect the graph.

    • Stretching and Shrinking: Adjusting the vertical or horizontal stretch of a function.

  3. Composition of Functions:

    • Combining functions; understand how to evaluate composite functions.

  4. Inverse Functions:

    • Finding inverses; a function is invertible if it passes the horizontal line test.

  5. Key Formulas and Properties:

    • Understand the characteristics and graphs of these types of functions.

    • Memorize important theorems related to function transformations and inverses.

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