3.1 Functions. X is called the independent variable Y is called the dependent variable.

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Presentation transcript:

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.

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

Form the following composite functions and state the domain.

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

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

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

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