7

Today:Warm-Up

Review Functions, Domain, & Range

Function NotationInterpreting Graphs

Warm-Up

2. Simplify: -3(5x - 3) -2(6x - 6)

4. Solve for b: A = ½b • h

3. Find the length & width:

1. - -3(8) -2 + -(4)

2x + 10

x P = 68

Vocabulary:1. Discreet Data: Data that has a limited number of values, with space between each value. Usually whole numbers.2. Continuous Data: Data with values that vary continuously over the graph. Data that is unbroken by space between values.

Examples:1. The number of suitcases lost by an airline:

2. The growth of corn plants:

3. The number of ears of corn harvested.

Mapping to Determine a Function

Create a mapping of the following relation and state whether or not it is a function.

{(-1,2) ; (1, 2) ; (5, 3) ; (6, 8)}

Notice that even though there are two 2’s in the range, you only list the 2 once.

-1

1

5

6

2

3

8

This relation is a function because each x-value maps to only one y-value. It is still a function if two x-values go to the same y-value.

Examples of the Vertical Line Test

function

function

Not a function

Not a function

……….

Graphing from an EquationGraph the line y = 2x + 3

The easiest way is to create a table, use numbers such as -2, -1, 0, 1, and 2 for x. Then solve for y and plot the points

……….

-2

-1

01

2

Function RulesThe equation that represents a function is called a function rule.

A function rule is written with two variables, x and y.

When you are given a function rule, you can evaluate the function at a given domain value to find the corresponding range value.

……….

How to Evaluate a Function RuleTo evaluate a function rule, substitute the value in for x and solve for y.

Examples: Evaluate the given function rules for x = 2

y = x + 5 y = 2x -1 y = -x + 2

y =(2)+ 5

y= 7

y = 2(2)-1

= 4 – 1

y= 3

y = -(2)+2

= -2 + 2

y= 0

……….

Evaluating for a Given DomainYou can also be asked to find the range values for a given

domain.

This is the same as before, but now you’re evaluating the same function rule for more than one number.

The values that you are substituting are x values, so they are a part of the domain.

The values you are generating are y-values, so they are a part of the range.

……….

Find the range values of the function for the given domain.

y = 5x - 7 ; {-3, -2, 4}

y = 5x -7 y = 5x -7 y = 5x - 7 y = 5(-3) - 7 y= 5(-2) -7 y = 5(4) - 7 y = -15 - 7 y= -10 - 7 y= 20 - 7 y= -22 y= -17 y= 13

The range values for the given domain are: { -22, -17, 13}

……….

Function Notation: f(x)..g(x)..h(x)Functions that can be written as equations can be written in function notation. The variable y and the term f(x) represent the dependent variable. It is simply a way to show that the y variable is a function of, or depends on x. It is read "f at x"Since x can be any number, the f(x) is the output, (the dependent variable), when a number is substituted for x.

Practice

1. Find the range values of the function

for the given domain.

f(x) = 3x + 1 ; {-4, 0, 2}

2. Find the range values of the function

for the given domain.

f(x) = -2x + 3 ; {-5, -2, 6}

Steps

1. Sub in each domain value in one @ a time.

2. Solve for y in each

3. List y values in braces.

Interpreting the Graph

Time (Seconds)

Graph 1

Height

Height

People

A. Cost of a laptop, past 10 years B. Drag racing before hitting tree

C. World Population, last 700 years D. Person's height during lifetime

E. 3-point shot F. Running up, then down a hill

Graph 3

Cost

Time (Years) Time (Decades)

Graph 2

Speed

Time (Seconds)

Speed

Time (Seconds) Time (Years)

Class Work:

Complete 3-2;Lessons 4-3 to 4-6 all

PracticeComplete the following questions:

1. Identify the domain and range of the following relations: a. {(-4,-1) ; (-2, 2) ; (3, 1) ; (4, 2)}b. {(0,-6) ; (1, 2) ; (7, -4) ; (1, 4)}

2. Graph the following relations and use the vertical line test to see if the relation is a function. Connect the pairs in the order given.

a. {(-3,-3) ; (0, 6) ; (3, -3)}b. {(0,6) ; (3, 3) ; (0, 0)}

3. Use a mapping to see if the following relations are functions: a. {(-4,-1) ; (-2, 2) ; (3, 1) ; (4, 2)}

b. {(0,-6) ; (1, 2) ; (7, -4) ; (1, 4)}

Answers:

1a. Domain: {-4, -2, 3, 4} Range: {-2, 2, 1}

1b. Domain: {0, 1, 7} Range: {-6, 2, -4, 4}

2a. 2b.

3a. 3b.

Function Not a Function

-4

-2

3

4

-1

2

1

0

1

7

-6

2

-4

4

FunctionNot a

Function

Examples

Find the range values of the function for the given domain.y = -3x + 2 ; {-1, 0, 1, 2}

The range values for the given domain are { 5, 2, -1, -4}.

Steps

1. Sub in each domain value in one @ a time.

2. Solve for y in each

3. List y values in braces.

y = -3x + 2 y = -3(-1) + 2 y = 3 + 2 y = 5

y = -3x + 2

y = -3(0) + 2

y = 0 + 2

y = 2

y = -3x + 2 y = -3(1) + 2y = -3 + 2y = -1

y = -3x + 2 y = -3(2) + 2y = -6 +2y = -4