Chapter 7.6, Problem 2P

Determine whether each table or rule represents a linear or an exponential function. Explain.

To determine

Whether the given table represents a linear or exponential function.

Answer to Problem 2P

The table represents a linear function $y=6x-3$ .

Explanation of Solution

Given information:

The table for function $y=f\left(x\right)$ is given below:

  

Method used:

From the given data a relationship between x and y is observed.

From the table, we observe that there is a common difference 6 between the values of y .

Therefore, the relationship between x and y is not exponential.

Further, observe that the values of y, 3, 9, 15, 21 are in arithmetic series whose first term is 3 and common difference 6.

The nth term of series $a+(a+d)+(a+2d)\dots$ is $T_n=a+\left(n-1\right)d$ .

Now, taking $n=x$ and $T_n=y$ , the xth term of the series is

  $y=3+\left(x-1\right)6$

  $\Rightarrow y=3+6x-6$

  $\Rightarrow y=6x-3$ , that is a linear relation between x and y .

Thus, the table represents a linear function $y=6x-3$

Conclusion:

The table represents a linear function $y=6x-3$ .