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Video: Determining If a Function Represents a Linear or Nonlinear Function given a Function Table

Bethani Gasparine

The table shows the charge for a long distance call as a function of the number of minutes the call lasts. Determine whether the charge is a linear or a nonlinear function of the number of minutes.<Table>

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Video Transcript

The table shows the charge for a long-distance call as a function of the number of minutes the call lasts. Determine whether the charge is a linear or a nonlinear function of the number of minutes.

In order for a function to be linear, it would need to have a constant rate of change. If it were nonlinear, it would not have a constant rate of change.

In order to find the rate of change, we need to look at our table. From three minutes to six minutes, that’s an increase in three minutes. From six minutes to nine minutes, that’s an increase in three minutes. And from nine minutes to twelve minutes, that’s an increase in three minutes.

Looking at the cost in cents, from 51 cents to 102 cents, that’s an increase in 51 cents. From 102 cents to 153 cents, that’s an increase in 51 cents. And from 153 cents to 204 cents, that’s an increase in 51 cents.

So this means an extra three minutes will cost an extra 51 cents. The increase from three minutes to six minutes cost an extra 51 cents. From six minutes to nine minutes, that cost an extra 51 cents. And from nine minutes to twelve minutes, that cost an extra 51 cents.

And each of these minutes were in increments of three minutes. So for every three minutes extra, it cost an extra 51 cents.

So what is that constant rate of change? Well for every one minute that is extra, it would be 17 cents. And how would we get that? Well if three minutes is 51 cents, we can take 51 divide by three.

This means every extra minute will cost an extra 17 cents. So since we have a constant rate of change, this would be a linear function.