fire up! with your neighbor, simplify the following expression and be ready to share out ! ready go!...
TRANSCRIPT
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