Unit 3 – Ch. 4

1. Unit 3 – Ch. 4 • 4.1/4.2 – Operations & Composite Functions • 4.3 – Reflecting Graphs (Symmetry) • 4.4 – Periodic Functions • 4.5 – Inverse Functions • Quiz 4.1-4.3 • Test Ch. 4

2. 4.1/4.2 Operations of Functions

3. Learning Objectives • Perform Operations on Functions • Find a Rule & Given Domain • Composite Functions • Find a Rule & Give Domain

4. Introduction to functions • Function • Pass the Vertical Line Test • NO More than one y for each x • Domain (algebraically) • Where fnct is restricted: • Square Root (vertex) • Cube Root (all reals) • Rational (all reals except…. set denominator =0) Don’t worry about range…

5. Function operations • Why should we care? • Use function operations to find difference in cost of production and revenue generated • Function Operations(f and g are functions) • Sum (f+ g)(x) = f (x) + g(x) • Difference: (f - g)(x) = f (x) - g(x) • Product: (f × g)(x) = f (x) × g(x) • Quotient: (f/g)(x) = • If g(x) = 0 , then the quotient is undefined

6. Function operations • Example: Find a Rule for a Function • Let 4 and . Find a rule for each of the following functions AND the domain:

7. Composition Functions • The composite of f and g is defined by two conditions: • Substitution • Domain of Composite • x is in the domain of g • g(x) is in the domain of f • DO NOT ASSUME • only true sometimes…

8. composition functions Example: Find Rules of Composite Functions • Let and • Find a rule for • Find the Domain for • Let and • Determine whether or not • Find the domains of both composite functions