004 Sample Final A, Problem 9

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Graph the function. Give equations of any asymptotes, and list any intercepts.     

Foundations
What are the vertical asymptotes of ?
Answer:
The vertical asymptotes are where is undefined.


Solution:

Step 1:
Since , the vertical asymptotes are and .
Step 2:
The horizontal asymptote is .
Step 3:
There is no intercept since for any .
Plugging in , we get . So, the intercept is (0,3)
Final Answer:
The vertical asymptotes are and . The horizontal asymptote is . There is no intercept and the intercept is (0,3).

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