2. The Reciprocal Function Family
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We want to draw the asymptotes and the graph of the given function. We will start by considering some possible transformations.
Transformations of f(x)=x1,x=0 | |
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Vertical Translations | Translation up k units, k>0y=x1+k
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Translation down k units, k>0y=x1−k
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Horizontal Translations | Translation right h units, h>0y=x−h1
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Translation left h units, h>0y=x+h1
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Let's apply these transformations one at a time. We will start by translating the parent function, f(x)=x1, 2 units right.
The last transformation is a vertical translation of 5 units up.
Finally, let's look at the graph of the given function and its asymptotes alone.