3.1 Functions x is called the independent variable

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Presentation transcript:

3.1 Functions x is called the independent variable y is called the dependent variable

Domain on Operations

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 Find each of the following

Form the following composite functions and state the domain.

Form the following composite functions and state the domain.

Form the following composite functions and state the domain.

Find possible functions for f and g Decomposition Find possible functions for f and g

5.2 Inverse Functions

Inverse Relations If (x, y) is on the graph of a relation, then (y, x) is on the graph of its inverse.

Inverse Relations

One to One Functions A function is one-to-one if every x has exactly one y-value and every y has exactly one x-value One to One Function

Not a One to One Function Other Relations Not a One to One Function Not aFunction

Horizontal Line Test 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

Inverse Functions

Inverse Functions

Show that the functions are inverses of each other Inverse Functions Show that the functions are inverses of each other