Step 1:

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The function is $\"\"$ , $\"\"$ and $\"\"$ . \ \

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The domain of a function is all values of $\"\"$ , those makes the function mathematically correct.

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The denominator of the function should not be zero.

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$\"\"$

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$\"\"$ .

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$\"\"$

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The domain of function is all real numbers except $\"\"$ and $\"\"$ .

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The domain of function is $\"\"$ .

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Rewrite the function as $\"\"$ .

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Cancel common terms. \ \

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$\"\"$ .

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The removable discontinuity is at $\"\"$ .

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Find the left hand limit at $\"\"$ is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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The hole is at $\"\"$ . \ \

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The function is continuous every number in its domain.

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$\"\"$ is in the domain and $\"\"$ is not in the domain. \ \

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The function is continuous at $\"\"$ .

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Step 2:

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Graph the function: \ \

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$\"\"$ \ \

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Observe the graph: \ \

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As $\"\"$ tends to 1 from the left hand side the limit approaches to $\"\"$ .

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$\"\"$ .

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As $\"\"$ tends to 1 from the right hand side the limit approaches to $\"\"$ .

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$\"\"$ .

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The vertical asymptote at $\"\"$ . \ \

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The hole at $\"\"$ . \ \

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Solution: \ \

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$\"\"$ .

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$\"\"$

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$\"\"$

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The hole at $\"\"$ .

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The vertical asymptote at $\"\"$ . \ \