Chapter 6.3, Problem 29E

To determine

To justify: Using graph of a set of points enough to determine linear or exponential function.

Answer to Problem 29E

Yes, we can determine whether the points represent linear or exponential function.

Explanation of Solution

Given information :

Given any data points.

Concept used:

Use patterns between consecutive data pairs to determine type of function.

Linear function: - The difference of consecutive y-values is constant.

Exponential function: - Consecutive y-values have a common ratio. In each case, the differences of consecutive x-values need to be constant.

Given a set of points, we can determine whether they represent a linear functions if when $x$ increases by a constant value, $y$ also increases or decreases by a constant value.

Also, we can determine whether they represent an exponential function if when $x$ increases by a constant value, $y$ is multiplied by a constant factor.

Hence,

Yes, we can determine whether the points represent linear or exponential function.