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The function is $\"\"$ .

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(a)

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Domain of a function is all possible $\"\"$ values.

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The rational function is undefined when $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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If $\"\"$ , then $\"\"$ , which is undefined.

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The speed of light $\"\"$ cannot be equal to the speed of the object $\"\"$ .

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Also $\"\"$ cannot be greater than $\"\"$ . Other wise, we would have to find the square root of a negative number, which is an imaginary number.Lastly, the speed cannot be less than zero because speed cannot be negative.

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If $\"\"$ , $\"\"$

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Domain is $\"\"$ .

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(b)

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Find $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ is the speed of the light $\"\"$ million meters per second.

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$\"\"$ .

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$\"\"$ .

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Find $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Find $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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(c)

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Describe the behavior of $\"\"$ as $\"\"$ approches $\"\"$ .

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$\"\"$ , since as $\"\"$ approches $\"\"$ , $\"\"$ approches $\"\"$ , making $\"\"$ very small. $\"\"$ divided by a very small number results in a very large quotient.

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As $\"\"$ approches $\"\"$ , $\"\"$ approches $\"\"$ .

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(d)

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Decompose the function into two separate functions.

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Let $\"\"$ and $\"\"$ .

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$\"\"$

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Replace $\"\"$ with $\"\"$ .

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$\"\"$

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Substitute $\"\"$ for $\"\"$ in $\"\"$ .

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$\"\"$ .

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(a) Domain is $\"\"$ .

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(b) $\"\"$ , $\"\"$ and $\"\"$ .

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(c) $\"\"$ , sincs as $\"\"$ approches $\"\"$ , $\"\"$ approches $\"\"$ , making $\"\"$ very small. $\"\"$ divided by a very small number results in a very large quotient.

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As $\"\"$ approches $\"\"$ , $\"\"$ approches $\"\"$ .

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(d) Let $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$ .