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