Functions and their Operations

1. Functions and their Operations Integrated Math 4 Mrs. Tyrpak

2. 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 inputs Range – set of outputs

3. Example: Temperature: Time of Day: Domain: Range: Ordered Pairs:

4. Numerically: Determine whether each of the following relations is a function. Identify the domain and range. • {(9, -5), (9, 5), (2, 4)} b) {(-2,5), (5,7), (0,1)} c) {(-5, 3), (0,3), (6,3)}

5. 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?

6. Function Notation f(x) = x + 3 f is the name of the function x 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”

7. Evaluating Functions

8. 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 • the function at that value does not exist • that input value is not in the domain of a function

9. Red Flags that Effect Domains

10. Find the domain of each function.

11. 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:

16. Thanks for your attention! Don’t forget to complete both the extension and enrichment assignments before you move on. Keep up the hard work!