Pearson Algebra 2 Common Core, 2011
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Pearson Algebra 2 Common Core, 2011 View details
2. The Reciprocal Function Family
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Exercise 20 Page 512

We want to draw the asymptotes and the graph of the given function. We will start by considering some possible transformations.

Transformations of
Vertical Translations
Horizontal Translations
Note that if the graph of the function is translated, the asymptotes are also translated in the same distance and direction. Consider the function.
The given function is a combination of transformations.
  • Horizontal translation units right
  • Vertical translation up units

Let's apply these transformations one at a time. We will start by translating the parent function, units right.

The last transformation is a vertical translation of units up.

Finally, let's look at the graph of the given function and its asymptotes alone.

We can see that the vertical asymtpote is the line and the equation of the horizontal asymptote is Using this information, we can state the domain and range of the function.