$\"\"$

Determine whether the given function is linear or non linear.

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

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

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\"\"

\"\"

Average rate of change

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

$\"\"$

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

$\"\"$

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

$\"\"$

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

$\"\"$

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

$\"\"$

Observe the table.

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

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

$\"\"$

The function is non-linear.