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.
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.
Composition of Functions:
Combining functions; understand how to evaluate composite functions.
Inverse Functions:
Finding inverses; a function is invertible if it passes the horizontal line test.
Key Formulas and Properties:
Understand the characteristics and graphs of these types of functions.
Memorize important theorems related to function transformations and inverses.