FIRE UP!

• With your neighbor, simplify the following expression and be ready to share out ! Ready GO!

• (x + 3)2

WEDNESDAY

Graphing Parent Functionsand

Functional Notation

Chapter 1

Section 1-2,3,5

Objectives• I can sketch parent function

graphs using critical points

• I can find functional values of any function

–From an equation

–From a graph

Functions

• A function is a special relation in which each element from the domain is paired with exactly one element from the range.

FunctionA 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.

Function Not a Function7 49 2 4 7 5 7 0 0 6 32 4 8 2

SOLUTION

GUIDED PRACTICE for Example 2

Tell whether the pairing is a function.

1221Output

12963Input2.

369

12

1221

The pairing is a function because each input is pairedwith exactly one output.

Parent Functions• These are the 8 parent functions for this unit!!

– Constant– Linear– Quadratic– Cubic– Absolute Value– Square Root– Reciprocal– Greatest Integer

Critical Points• You must graph all the critical

points for each function!

• 10x10 Grid all year

Graph: f(x) = 0

Constant

Linear

• What are critical points

X y

0 0

1 1

-1 -1

2 2

-2 -2

3 3

-3 -3

( )f x x

Graph: f(x) = x

Linear

Quadratic

• What are critical points

X y

0 0

1 1

-1 1

2 4

-2 4

3 9

-3 9

2( )f x x

Graph: f(x) = x2

Quadratic

Graph: f(x) = 1

x

Reciprocal

Square Root

• What are critical points

X y

0 0

1 1

4 2

9 3

16 4

( )f x x

Graph: f(x) = x

Square Root

Functional Notation

• Functional notation is a way to express an equation as a function

• If we have an equation y = 2x + 3• We can write this in functional notation as:• f(x) = 2x + 3• f(x) replaces the y • It is read “f of x”• x is the input and f(x) is the output

Finding a Functional value• f(x) = 6x + 10• Find f(-3)• This means substitute –3 for all x variables and evaluate• f(-3) = 6(-3) + 10 = -18 + 10 = -8• g(x) = 2x2 + 4x – 1• Find g(-3)• g(-3) = 2(-3)2 + 4(-3) – 1 • 2(9) + (– 12) – 1 • 18 – 12 – 1• 5

What does this mean?

• f(3)

• This reads as “ f of 3”

• Simply put: “What is the y-value for an

x-input of 3

SOLUTION

EXAMPLE 5 Evaluate functions

Evaluate the function when x = – 4.

a. f (x) = – x2 – 2x + 7

f (x) = – x2 – 2x + 7 Write function.

f (– 4) = –(– 4)2 – 2(– 4) + 7 Substitute –4 for x.

= –1 Simplify.

Practice Problem Given  f(x) = x2 + 2x – 1, find  f(2).

Practice Problem

Practice Problem

Practice Problem

Given  f(x) = x2 + 2x – 1, find  f(–3).

f(2) = (2)2 +2(2) – 1      = 4 + 4 – 1      = 7

f(–3) = (–3)2 +2(–3) – 1      = 9 – 6 – 1      = 2

Evaluate f(@).

Given  f(x) = x2 + 2x – 1 f(@) = (@)2 + 2(@) – 1 = @2 + 2@ – 1.

Given that f(x) = 3x2 + 2x, find f(h).

f(h) = 3(h)2 + 2(h) = 3h2 + 2h

From a Graph

• You can also pick functional values from a graph

• Remember f(x) replaced “y”

• So, you are just finding y-values corresponding to the x-values

(1)f 1( 1)f 1

( 2)f 0

(4)f 3

(2)f 4What does this mean?

Does Not Exist (DNE)

(1)f 1( 3)f 5( 6)f 2(0)f 2

(11)f DNE

Step It Up

2( ) 3f x x x

Find f(x + 2)

2 2x x

Homework

WS 1-2

Signed Paperwork and Supplies if you forgot

Work on Parent Function Packets