FUNCTION NOTATION AND EVALUATING FUNCTIONS

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

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

Sometimes we will only know one part of the ordered pair 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

b. ( ?, 9 ) What is ____ if _________? (0, 9) -9

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

Does not mean multiplication! Function notation replaces the dependent 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 Function Notation Read as is read as “ ___________________________________” Function Notation Read as

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

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

Changes the domain into the range The numbers of the domain are sometimes called the ________ and the range is called the ___________. input output 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 }. range domain Range = { } Domain Range 2 4 1 7 13 Written as ordered pairs:

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

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

Try these… If find: A. . B. .

Functional Notation An equation that is a function may be expressed using functional notation. The notation f(x) (read “f of (x)”) represents the variable y.

Functional Notation Cont’d Example: y = 2x + 6 can be written as f(x) = 2x + 6. Given the equation y = 2x + 6, evaluate when x = 3. y = 2(3) + 6 y = 12

Functional Notation Con’t For the function f(x) = 2x + 6, the notation f(3) means that the variable x is replaced with the value of 3. f(x) = 2x + 6 f(3) = 2(3) + 6 f(3) = 12

Evaluating Functions Given f(x) = 4x + 8, find each: f(2) 2. f(a +1) = 4(2) + 8 = 16 = 4(a + 1) + 8 = 4a + 4 + 8 = 4a + 12 = 4(-4a) + 8 = -16a+ 8

Determine the value of x when given f(x). Given f(x) = 4x + 8, determine x when: f(x) = 2 f (x) = -1

Evaluating More Functions If f(x) = 3x  1, and g(x) = 5x + 3, find each: 1. f(2) + g(3) = [3(2) -1] + [5(3) + 3] = 6 - 1 + 15 + 3 = 23 2. f(4) - g(-2) = [3(4) - 1] - [5(-2) + 3] = 11 - (-7) = 18 3. 3f(1) + 2g(2) = 3[3(1) - 1] + 2[5(2) + 3] = 6 + 26 = 32