005 Sample Final A, Question 2

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Question Find the domain of the following function. Your answer should be in interval notation

Foundations:
1) What is the domain of ?
2) How can we factor ?
Answer:
1) The domain is . The domain of is , but we have to remove zero from the domain since we cannot divide by 0.
2)


Step 1:
We start by factoring into
Step 2:
Since we cannot divide by zero, and we cannot take the square root of a negative number, we use a sign chart to determine when
Step 3:
Now we just write, in interval notation, the intervals over which the denominator is positive.
The domain of the function is:
Final Answer:
The domain of the function is:

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