$\"\"$

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The function is $\"\"$ .

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

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If $\"\"$ , the function is $\"\"$ .

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$\"\"$ is continuous on the interval $\"\"$ .

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If $\"\"$ , the function is $\"\"$ .

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$\"\"$ is continuous on the interval $\"\"$ .

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Now observe the graph :

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Here $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$ .

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Hence the function is discontinuous at $\"\"$ .

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The domain of the function is continuous for all values of $\"\"$ except $\"\"$ .

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$\"\"$

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The function is $\"\"$ .

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If $\"\"$ , the function is $\"\"$ .

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Limit definition of derivatives : $\"\"$ .

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$\"\"$

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$\"\"$ .

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If $\"\"$ , the function is $\"\"$ .

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Limit definition of derivatives : $\"\"$ .

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$\"\"$

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$\"\"$ .

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The derivative of the function is $\"\"$ .

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The domain of the derivative function is continuous for all values of $\"\"$ except $\"\"$ .

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$\"\"$ is not differentiable at $\"\"$ .

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$\"\"$

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$\"\"$ is not differentiable at $\"\"$ .