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2.3 Transformation

Tags
Transformation
Functions
Domain
Range
Asymptotes
Graph
Reflection
Scale factor
Translation
Stretch
There are 3 types of transformations to remember.
1.
Translation by (ab)\binom ab to obtain f(x−a)+bf(x-a)+b
a.
Horizontal translation by (a0)\binom a0 to obtain f(x−a)f(x-a)
b.
Vertical translation by (0b)\binom 0b to obtain f(x)+bf(x) + b
2.
Stretch by scale factor kk
a.
Horizontal stretch by scale factor kk to obtain f(1kx)f(\frac 1kx)
b.
Vertical stretch by scale factor kk to obtain kf(x)kf(x)
3.
Reflection
a.
Reflection by the yy-axis: f(−x)f(-x)
b.
Reflection by the xx-axis: −f(x)-f(x)
Figure 2.3.1 Graphical representation of vertical stretch by a factor of 2 (left) and horizontal transformation by 3 units and 1 unit vertically (right)
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2.3 Transformation