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