math 19a mind map

math 19a mind map

1. Functions

   • Example: f(x)=x^2
   • Definition: An expression which shows the relationship between one variable (independent variable) and another variable (dependent variable).
   • Ways to represent functions: (1) equations (algebraic), (2) graph, (3) table, (4) verbal description
   • Vertical Line Test:
   • Piecewise-defined functions: using different equations for different parts of their domain.
     • Example:
   • Increasing & decreasing functions
   • Combining Functions
   • Function Composition
   • Linear Functions
     • Finding slope:

2. Polynomials

   • Quadratic Formula: ax^2+bx+c=0
   • Root functions
   • Transcendental functions
   • Trignometric Functions

3. Inverse functions

   • One-to-one function
     • horizontal line test
   • Inverse trignometric functions
   • Limits of functions at finite numbers
     • One sided limits

4. Limits

   • Limits of polynomial and rational functions

5. Continuity

   • Continuity Theories
     • squeeze theorem
     • intermediate value theroem

6. Power Rule

7. Power Rule:

8. Product Rule

9. Quotient Rule

10. Average Rate of Change

11. Higher Order Derivatives

12. Chain Rule

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