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Allison Blanchard, Chris Eberz, and Jule Gamache

Final Exam Study Guide PreCalculus Review, L’Hopital’s Rule, Integration By Parts, Integration by Partial Fractions. Allison Blanchard, Chris Eberz, and Jule Gamache. Domain and Range. In order for a relation to be a function it must pass the vertical line test.

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Allison Blanchard, Chris Eberz, and Jule Gamache

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  1. Final Exam Study GuidePreCalculus Review, L’Hopital’s Rule, Integration By Parts, Integration by Partial Fractions Allison Blanchard, Chris Eberz, and Jule Gamache

  2. Domain and Range • In order for a relation to be a function it must pass the vertical line test. • Inverse of a function must pass the horizontal line test. • In order to be included in the domain of a function, the values must not make the denominator equal zero. • We can also only have nonnegative values in an even root.

  3. Domain and Range • Examples:

  4. Function Notation • For each function there is a set: one domain value corresponds with one range value. • Function Notation sets up an equation that allows one to easily find a range value by inputting a domain value. f∘gf∙g

  5. Function Notation • Examples:

  6. Function Notation • More Examples

  7. Function Notation • More Examples

  8. Operations with Functions • This applies function notation by using the arithmetic operations: • Addition • Subtraction • Multiplication • Division • Substitution (Plugging one into the another)

  9. Operations with Functions • Examples:

  10. Exponentials and Logarithmic Functions • Properties of Exponents

  11. Exponentials and Logarithmic Functions • Examples:

  12. Exponentials and Logarithmic Functions • Properties of Logs

  13. Exponentials and Logarithmic Functions • Examples

  14. Exponentials and Logarithmic Functions • Solving Equations Using Logs (Examples)

  15. Chapter 1 Quiz! • Domain and Range • Function Notation • Operations with Functions • Exponentials and Logarithmic Functions

  16. L’Hopital’s Rule

  17. L’Hopital’s Rule • Example

  18. Integration by Parts

  19. Integration by Parts • Examples

  20. Integration by Parts • More Examples

  21. Integration by Parts • More Examples

  22. Integration by Parts • More Examples

  23. Integration by Partial Fractions • Rules:

  24. Integration by Partial Fractions • Decomposition of Fractions Example

  25. Integrations by Partial Fractions • Repeating Linear Fractions Example

  26. Integration by Partial Fractions • Shortcut for Non-Repeating Example

  27. Post AP Exam Topics Quiz! • L’Hopital’s Rule • Integration by Parts • Integration by Partial Fractions

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