This document discusses operations that can be performed on functions, including sums, differences, products, and quotients. It notes that the domain of these operations must be considered. It also covers topics like graphing sums of functions, composite functions, and using calculators to help graph complex composite functions. Examples and exercises are provided to illustrate these concepts.

1. Sums and products of functions
SUM
DIFFERENCE
PRODUCT
QUOTIENT
The domain of the above operations→

2. Example 1.
Graphing sums of
functions will be
discussed in Section
3.9.
Exercise 1E 1, 2

3. Composite functions
Example 1.

4. In function composition, it is often necessary to check domains and ranges carefully
to determine whether they are defined.
However, as this is the new input for
f, it must be in the domain of f.

5. Example 1.
Composite functions can be rather complex
to graph by hand, so a CAS calculator can be
used for assistance when sketching.

6. The function f is applied first
and, then the modulus
function:
Example 5.

7. Example 5.
Exercise 1F 1, 2 (calc), 4, 5, 7, 8b, 9*, 10,
11, 13