1. 1.41.4 Combinations of Functions

2. Quick Review

3. What you’ll learn about Combining Functions Algebraically Composition of Functions Relations and Implicitly Defined Functions … and why Most of the functions that you will encounter in calculus and in real life can be created by combining or modifying other functions.

4. The Identity Function

5. The Squaring Function

6. The Cubing Function

7. The Reciprocal Function

8. The Square Root Function

9. The Exponential Function

10. The Natural Logarithm Function

11. The Sine Function

12. The Cosine Function

13. The Absolute Value Function

14. The Greatest Integer Function

15. The Logistic Function

16. Example Looking for Domains One of the functions has domain the set of all reals except 0. Which function is it?

17. Example Looking for Domains One of the functions has domain the set of all reals except 0. Which function is it?

18. Example Analyzing a Function Graphically

20. Sum, Difference, Product, and Quotient

21. Example Defining New Functions Algebraically

23. Composition of Functions

25. Example Composing Functions

27. Example Decomposing Functions

29. Example Using Implicitly Defined Functions