Functions and their Operations

Integrated Math 4

Mrs. Tyrpak

Definition of a Function

A function is a correspondence between a first set, called the domain, and a second set, called the range, such that each member of the domain corresponds to exactly one member of the range.

Domain – set of inputsRange – set of outputs

• Example:

Domain: Range:Ordered Pairs:

Time of Day: Temperature:

Numerically: Determine whether each of the following relations is a function. Identify the domain and range.

a){(9, -5), (9, 5), (2, 4)}

b) {(-2,5), (5,7), (0,1)}

c) {(-5, 3), (0,3), (6,3)}

Vertical Line Test: A set of points in a coordinate plane is the graph of a function if and only if no vertical line intersects the graph at more than one point.

Graphically: Which of the following graphs are functions?

Function Notation

f(x) = x + 3f is the name of the functionx is the input value of the function (also called the independent variable)f(x) is the output value of the function (also called the dependent variable)*f(x) is read “f of x” or “the value of f at x”

Evaluating Functions

Finding the domain

*Remember the domain is the set of all possible input values for which the function is defined*When an input value results in an expression that is not defined as a real number then 1)the function at that value does not exist 2)that input value is not in the domain of a function

Red Flags that Effect Domains

Find the domain of each function.

Operations of Functions

Let f and g be two functions with overlapping domains. Then, for all x common to both domains, the sum, difference, product, and quotient of f and g are defined as follows:

Thanks for your attention!

Don’t forget to complete both the extension and enrichment assignments

before you move on.

Keep up the hard work!