004 Sample Final A, Problem 5

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Describe how the graph of  can be obtained from a basic graph. Then sketch the graph. Provide at least two ordered pairs, and the equation of any asymptote.

Foundations
1) What is the basic graph of ?
2) How is the graph obtained from ?
3) How is the graph obtained from ?
Answer:
1) The basic graph is .
2) The graph of is obtained by shifting the graph of up 1 unit.
3) The graph of is obtained by shifting the graph of to the right by 3 units.


Solution:

Step 1:
We start with the basic graph of .
To get the graph of from , we shift the graph of down 2 and to the left by 1.
Step 2:
Two ordered pairs are (-1,-1), and (0,1). There is a horizontal asymptote at .
Final Answer:
To get the graph of from , we shift the graph of down 2 and to the left by 1.
Two ordered pairs are (-1,-1), and (0,1). There is a horizontal asymptote at

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