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Transcript of Transformation
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
graph is moving away from x-axis
a > 1
take absolute value to perform stretch
reflect over the x-axis
graph is moving away from the y-axis
0 < a < 1
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
Reflections over X- Axis
The output value changes.
Reflection across Y-Axis
The input value changes
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)
Right Shift- f(x)= f(x-a)
Examples Using Reflections
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
Move right 10 units f(x−3)=(x−3)^2
Move left 10 units f(x+3)=(x+3)^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.
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