1. Chapter 2: Analysis of Graphs of Functions
2.1 Graphs of Basic Functions and Relations; Symmetry 2.2 Vertical and Horizontal Shifts of Graphs 2.3 Stretching, Shrinking, and Reflecting Graphs 2.4 Absolute Value Functions 2.5 Piecewise-Defined Functions 2.6 Operations and Composition

2. Operations and Composition
Operations on Functions
Given two functions f and g, then for all values of x for which both f(x) and g(x) are defined, the functions f + g, f − g, fg, and f/g are defined as follows.

3. Examples Using Operations on Functions
Let f(x) = x2 + 1 and g(x) = 3x + 5. Perform the operations. a. (f + g)(1) b. (f − g)(−3) c. (fg)(5) d. (f/g)(0)

4. Examples Using Operations on Functions

5. Evaluating Combinations of Functions
If possible, use the given graph of f and g to evaluate (a) (f − g)(−2) (b) (f · g)(1) (c) (f / g)(0)

6. The Difference Quotient

7. Finding the Difference Quotient
Let f(x) = 2x2 − 3x. Find the difference quotient and simplify.

8. Finding the Difference Quotient
Let f(x) = 2x2 − 3x. Find the difference quotient and simplify.

9. Composition of Functions
If f and g are functions, then the composite function, or composition, of g and f is

10. Evaluating Composite Functions

11. Finding Composite Functions
Solution

12. Decomposing Composite Functions