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.