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Transformation

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by

Jenai Patrick

on 12 September 2013

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Transcript of Transformation

Transforming Functions
Definition of a Transformation
In other words, Moving a shape/line so that it is in a different position, but still has the same size, area, angles and line lengths.
Reflections Over X and Y-Axis
Vertical and Horizontal Stretch
Vertical Stretch
graph is moving away from x-axis
a > 1
2f(x)
if negative:
take absolute value to perform stretch
reflect over the x-axis
Horizontal Stretch
graph is moving away from the y-axis
0 < a < 1
f(0.5x)
If a is negative:
take absolute value to stretch
reflect over y-axis
Parent function - green
Horizontal stretch - red
Horizontal compression - blue
Parent Function - green
Vertical stretch - blue
Vertical compression - red
Example
Compression
Reflections over X- Axis
The output value changes.
f(x)----> -f(x)
Reflection across Y-Axis
The input value changes
f(x)---> f(-x)
Placing the edge of a mirror on the y-axis will form a reflection in the y-axis. This can also be thought of as "folding" over the y-axis.
Left Shift- f(x)= f(x+a)
Horizontal Translation/Shift
Right Shift- f(x)= f(x-a)

X-Axis
Examples Using Reflections
Y-axis
Vertical Shift
Example
A transformation where the function is made smaller (compressed).
Add/subtract a number to the function to move it up and down.
Move up: f(x)+D
Move down: f(x)–D
Example
f(x)=x^2
Move right 10 units f(x−3)=(x−3)^2
Move left 10 units f(x+3)=(x+3)^2
f(x)=x^2
Move up 2 units: f(x)+2=x^2+2
Move down 2 units: f(x)−2=x^2−2
Any figure which is moved from one location to another location on the coordinate plane without changing its shape, size, or orientation is called translation.
Example:
If the original (parent) function is y = f (x), the reflection over the x-axis is function -f (x).
Example: If the original (parent) function is y = f (x), the reflection over the y-axis is function f (-x).
When the coefficient is greater than 1, the function is compressed horizontally.

C > 1, f(x) = 2x
If the coefficient is less than 1, but greater than zero, the function is vertically compressed.

0 < C < 1,
f(x) = (1/2)x
Full transcript