Transformations

1
Section 2.5

• Transformations

2
Parent Functions
Cubic
linear
Quadratic
constant
Square Root
Rational
Absolute Value
Exponential
Logarithmic
3
Parent equations are the foundations to many of
our equations.
We can use transformational techniques to build
on them.
Where the variable is defines what is inside or
outside the function
It may help you to see this if you put the
variable in parenthesis.
inside
Remember, for
we would put x2 inside the parent function
4
Translations are like grabbing a graphing with
your cursor and changing them
5
TI-84
Vertical and Horizontal Translations
inside the function
outside the function
Addition or subtraction OUTSIDE move the function
some units vertically with the sign
Addition or subtraction INSIDE move the function
some units horizontally opposite the sign
6
Formal Definition
For bgt0
The graph of
is graph of
shifted up b units.
The graph of
is graph of
shifted down b units.
For dgt0
The graph of
is graph of
shifted right d units.
The graph of
is graph of
shifted left d units.
Garnerism outside means vertical true
direction inside
horizontal opposite direction
7
Reflections
a reflection is a graph and its image across an
axis
The graph of
is the graph of
We changed y to -y.
across the x-axis
The graph of
is the graph of
We changed x to -x.
across the y-axis
We are using symmetry
8
Vertical/Horizontal Stretch/Shrink
A key to understanding this aspect is to consider
rate of growth
Consider
What happen when
Garnerism outside means vertical direction
inside horizontal opposite
What happen when
9
TI-84
How transformed?
Outside
Inside
Stretch or compression
Stretch or compression
Outside
Inside
Stretch or compression
Stretch or compression
10
Parent form - Quadratic
Transformational Form
a and b are outside so they are VERTICAL
c and d are outside so they are HORIZONTAL
Outside uses true directions
Inside uses opposite directions
To reflect across x change y to -y
To reflect across y change x to -x
11
How transformed?
How transformed?
How transformed?
How transformed?
How transformed?
12
Homework

• 1,3,5,6,11,13,21,23,31,34,45,46,47,48