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