$\"\"$

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To determine whether the given function is linear or non-linear.

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First compute the average rate of change of $\"\"$ with respect to $\"\"$ and then compute the ratio of the consecutive outputs.

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If the average rate of change is constant, then the function is linear else non-linear.

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\"\"

\"\"

Average rate of change

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$\"\"$ $\"\"$

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$\"\"$

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$\"\"$ $\"\"$

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$\"\"$

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$\"\"$ $\"\"$

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$\"\"$

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$\"\"$ $\"\"$

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$\"\"$

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$\"\"$ $\"\"$

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$\"\"$

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Observe the above table.

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For the function, the average rate of change from $\"\"$ to $\"\"$ is $\"\"$ and from $\"\"$ to $\"\"$ is $\"\"$ .

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Since the average rate of change is not constant, the function is a non- linear function.

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$\"\"$

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The function is non-linear.