Ch1 math

Chapter 1 Functions

Domain = [0, ∞) Range = *0, ∞)

Conclusion and Definition • Not every relation is a function.

• Every function is a relation.

• Definition: Let X and Y be two nonempty sets.

A function from X into Y is a relation that associates with each element of X exactly one element of Y.

Types of functions (*7*) • • • • • • •

Algebraic Functions (4) Exponential Functions (3) Logarithmic Functions (3) Trigonometric Functions (6) inverse trigonometric Functions (6) hyperbolic Functions (6) Inverse Hyperbolic Functions (6)

Note that • In discrete math, we frequently use the following functions over real numbers: x (“floor of x”) is the largest integer  x. x (“ceiling of x”) is the smallest integer  x.

• Real numbers “fall to their floor” or “rise to their ceiling.”

• Note that if xZ, x   x & x   x • Note that if xZ, x = x = x.