3.1 Functions

X is called the independent variable

Y is called the dependent variable

Operations on Functions

Domain on Operations

Perform each mathematical operation and state the domain on

each operation.

Perform each mathematical operation and state the domain on

each operation.

A function is continuous over an interval of its domain if its hand-

drawn graph over that interval can be sketched without lifting the

pencil from the paper.

Discontinuous at x = -2

Continuous Function

5.1 Composite Functions

Composite Functions

Find each of the following.

Composite Functions

Composite Functions

Form the following composite functions and state the

domain.

Form the following composite functions and state the

domain.

Composite Functions

Composite Functions

Form the following composite functions and state the

domain.

Find possible functions for f and g.

Decomposition

5.2 Inverse Functions

If (x, y) is on the graph of a relation, then (y, x) is

on the graph of its inverse.

Inverse Relations

Inverse Relations

One to One FunctionsA function is one-to-one if

every x has exactly one y-value and every y has exactly one x-

value

Other Relations

If every horizontal line intersects the graph of a function f in at most

one point, then f is one–to–one.

Not One–to–One

One–to–One

Horizontal Line Test

Inverse Functions

Inverse Functions

Inverse Functions

Inverse Functions

Finding the inverse of a domain-restricted function

Inverse Functions

Finding the inverse of a domain-restricted function

If the inverse is not one-to-one, restrict the domain to make the

inverse correct.

Inverse Functions