FUNCTION NOTATION AND EVALUATING FUNCTIONS SECTIONS 5 1

FUNCTION NOTATION AND EVALUATING FUNCTIONS SECTIONS 5. 1 & 14. 1 B

relation is a set of _________. ordered pairs A ____ The ____ of ____ numbers domain is the ______ set first in a relation. The ____ is the ______ of ____ range set second numbers in a relation.

function A ______ is a relation in which no number in the domain repeated _____ is _____. Functions can be represented five different ways: mapping 1. _______ graph 2. _______ 3. _______ table Set of ordered pairs 4. _______ equation 5. _______

Sometimes we will only know one part of the ordered pair. We can use the equation to find the missing number. Example 1: Complete each ordered pair so that it is a solution to a. ( 1, ? ) What is ____ if _____? (1, 7) -2

TRY THIS…. c. ( 4, ? ) What is ____ if _____? (4, 1) -8

Function notation replaces the independent variable, y with either f(x), g(x), or h(x). f _____ of _____” x f(x) is read as “ ____ Does not mean multiplication! g _____ of _____” x g(x) is read as “ ____ h _____ of _____” x h(x) is read as “ ____

Instead of writing, , we replace the y with is read as “ __________________” Function Notation Read as

Look at the mappings below. is happening to What is happening to each number in the. What domain to get the x to get the corresponding number in the range? Domain Range 2 8 5 11 10 16 Domain Range -3 -6 0 0 5 10 corresponding f(x) value? Function Rule: What is happening to x to get the corresponding f(x) value? Function Rule:

function rule can be thought of as an operation that changes the The _______ numbers in the ______ to make the ____. domain range Function notation: function rule The right side of any function notation is called the _______. Replace the y with f(x) Equation Function Notation Right side of notation Function Rule

input The numbers of the domain are sometimes called the ____ and the output range is called the ______. Changes the domain into the range input output Function Rule

Find the range for the function if the domain of f(x) is { 0, 2, 4 }. domain Range = { } range Domain Range 0 1 2 7 4 13 Written as ordered pairs:

Try this… , find the range For the function, if the domain is { -3, 0, 4 }. Input Output = = = Range:

Sometimes we only want to only evaluate one element of the domain. For example, if “find when ”, can be written in a shorter form as “ find Example 2: If . ”. Plug 2 into the function rule.

Try these… If find: A. . B. .