as a transformation of 
using shift up of 17 units followed by shift to right of 2 units.y=2/(x+3) as a trasnformation of y=1/x using a shift left of 3 units followed by a vertical stretch of 2 units.
Graphical Transformations
With practice, you will use the ideas from Section 1.6 to construct by hand graphical representations of more complicated function from the 12 Basic Functions. This will help you get rough sketches by hand of things like:
as a transformation of using shift up of 17 units followed by shift to right of 2 units.
y=2/(x+3) as a trasnformation of y=1/x using a shift left of 3 units followed by a vertical stretch of 2 units.
I am using a computer to get the plots, but ultimately you would be doing this by hand.
First Example: Absolute Value Basic Function
Original Function
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Vertical Shift
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Horizontal Shift
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Vertical Stretch
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Horizontal Compression
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Reflection about x-axis
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Reflection about y-axis
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Second Example: Cubing Basic Function
Original Function
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Vertical Shift
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Horizontal Shift
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Vertical Stretch
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Horizontal Compression
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Reflection about x-axis
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Reflection about y-axis
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Third Example: Inverse Basic Function
Original Function
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Vertical Shift
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Horizontal Shift
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Vertical Stretch
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Horizontal Compression
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Reflection about x-axis
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Reflection about y-axis
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Fourth Example: Combining multiple transformations
Original Function
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Vertical Shift of 3 units up
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Vertical Shift of 3 units up followed by
Horizontal Shift of 2 units to the left
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Vertical Shift of 3 units up followed by
Horizontal Shift of 2 units to the left followed by
Reflection about x axis
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The Algebraic representation of the final function
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In[170]:=
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Fifth Example: Combining multiple transformations for 
:
shift to right 5 units, then
compress horizontally by 3 units, then
reflect about y-axis.
Original Function
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Shift 5 units to right
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then Compress horizontally by 3 units
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then reflect about the y-axis
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The algebraic representation of the final function is
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Sixth Example: Combining multiple transformations for f(x)=1/x to sketch y = 5/(x + 3)
Original Function
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The algebraic representation of the final function is
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Shift 3 units to right
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then vertical stretch of 5 units
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