CSci 271 Lecture Notes
Week Three, Monday: Functions
Introduction to Functions
Definition 1:
A function from a set A to a (possibly the same) set B is an assignment
of exactly one element of B to each element of A. For example, f(a) =
b where b is the unique element of B assigned by the function f to the element a
of A. We can also write f : A --> B (read that "f is a function mapping A to B").
Definition 2:
If f : A --> B we say that A is the domain of f and B is the codomain
of f. If f(a) = b we say b is the image of a and a is the preimage of
b. The range of f is the set of all images of elements of A.
Definition 3:
(addition and multiplication of functions, see text)
Definition 4:
(the image of a subset of the domain, see text)
One-to-One and Onto Functions
Definition 5:
(one-to-one, or injective, see text)
Definition 6:
(strictly increasing or decreasing, see text)
Definition 7:
(onto, or surjective, see text)
Definition 8:
(one-to-one correspondence, or bijective, see text)
Inverse Functions and Compositions of Functions
Definition 9:
(inverse function, see text)
Definition 10:
(composite functions, see text)
Graphs of Functions
Definition 11:
(graph of a function, see text)
Some Important Functions
Definition 12:
(floor and ceiling functions, see text)
Homework Solutions Discussion
We will discuss any problems and exercises there are questions on.
Chapter 1.1: 1, 2, 3, 6, 8, 10, 14, 18, 22.
Chapter 1.2: 6, 18.
Chapter 1.3: 10, 14, 20.
This page established September 18, 1998; last updated September 18, 1998.