warm up 8/2
DESCRIPTION
Warm up 8/2. For each function, evaluate f(0), f(1/2), and f(-2) f(x) = x 2 – 4x f(x) = -2x + 1 If f(x) = -3x, find f(2x) and f(x-1) If f(x) = -2x + 3, find f(-2x) and f(2x-1). Answers. f(0)=0, f(1/2)=-1.75, f(-2)=12 =1, =0, =5 -6x , -3x + 3 4x + 3, -4x + 5. - PowerPoint PPT PresentationTRANSCRIPT
Warm up 8/2
For each function, evaluate f(0), f(1/2), and f(-2)
1.f(x) = x2 – 4x2.f(x) = -2x + 13.If f(x) = -3x, find f(2x) and f(x-1)
4.If f(x) = -2x + 3, find f(-2x) and f(2x-1)
Answers
1) f(0)=0, f(1/2)=-1.75, f(-2)=12
2) =1, =0, =5
3) -6x , -3x + 3
4) 4x + 3, -4x + 5
Lesson 1.8 Transformations
A translation is type of transformation where a graph is
moved horizontally and/or vertically.
What is a translation?
The graph moves horizontally (h) units and vertically (k) units
So f(x) = (x-h) + k
Given the graph f(x)=(x-h)+k.
Left/right
Opposite of h
Up/down
Example 1:If the pre-image (original) is f(x) = 2x, Describe the translation of the image of
f(x) = 2(x – 3)+ 4. h = _____ which means _____________ k = _____ which means______________
3
4
3 units to the right
4 units up
Example 2: Pre-image f(x) = 3x
Image f(x) = 3(x+2) - 3
Describe the translation.
left 2, down 3
Example 3: Write the new equation.
up. units 4 andleft units 2 translated
is 3
1)(graph The xxf
4)2(3
1)( xxf
Example 4: Given f(x) = -4x. A. Find f(x+5). -4(x+5) -4x – 20
B. Find f(x-1)+6. -4 (x-1)+6 -4x +4 + 6 -4x + 10
Example 5:
The pre-image is the blue function defined as y =x
a) What would be the equation of the red function?
b) What would be the equation of the green function?
y = x + 3
y = (x – 3) – 1
Another type of transformation is a REFLECTION…
Reflection across the y-
axis
Reflection across the x-
axis
Each point flips across the y-axisThe x-coordinate changes(x,y) (-x, y)
Each point flips across the x-axisThe y-coordinate changes(x,y) (x,-y)
Translating and Reflecting Functions
Use a table to perform each transformation of
y = f(x).
a) Translation 2 units down
b) Reflection across the y-axis
Stretches and Compressions
Horizontal Vertical
Stretch
Each point is pulled away from the y-axis. The x-coordinate changes.(x, y) (bx, y)
Each point is pulled away from the x-axis. The y-coordinate changes.(x, y) (x, by)
Compression/Shrink
Each point is pushed toward the y-axis. The x-coordinate changes.(x, y) (bx, y)
Each point is pushed toward the x-axis. The y-coordinate changes.(x, y) (x, by)
Use a table to perform a horizontal compression of y = f(x) by a factor of ½.
The Parent Function is the simplest function with the defining characteristics of the family. Functions in the same family are transformations of their parent functions.
Lesson 1.9 - Intro to Parent Functions
Parent Functions
Family
Rule
Domain
Range
quadratic
f(x) = x2
y ≥ 0
constant
f(x) = c
y = c
Linear
f(x) = x
x x
y
x
Parent Functions
Cubic
f(x) = x3
Square Root
x ≥ 0
y ≥ 0
( )f x x
Family
Rule
Domain
Range
x
y
Identify the parent function and describe the transformation
( )f x x
( ) 2f x x
1.3.
2.
f(x) = x2
Up 4
f(x) = x2 + 4
f(x) = x
Down 3
f(x) = x-3
( )
2
( ) 2
f x x
Right
f x x
Find the parent function and the transformation
x -4 -2 0 2 4
y 8 2 0 2 8
1. Graph it
Parent function: f(x) = x2
2. Look at some points. Compare (2,2) with (2,4) from the parent function.
Both x values are the same. Starting with the 4 (parent function) what did we do to = 2?
4/2 = 2
So each y value was divided by 2. That is a vertical compression