Chapter 4.3, Problem 7PPE

To determine

To sketch: the graph of the function shown by given table and to find whether the function is linear or nonlinear.

Answer to Problem 7PPE

The function is nonlinear.

Explanation of Solution

Calculation:

Consider below table. It represents the length $L$ of a pencil in inches is a function of time $t$ in seconds it has been sharpened.

Pencil Sharpening
$t$	0	3	6	9	12	15
$L$	7.5	7.5	7.5	7.5	7.4	7.3

Using the above table, make a graph. Here, dependent variable is length of pencil and independent variable is time for which pencil sharpened. Thus, write $t$ values on horizontal axis and $L$ values on vertical axis.

Graph is as follows-

  

A nonlinear function is a function whose graph is not a line of part of a line.

Observe the graph. Found that, this is a curve not a line.

Thus, the function is nonlinear.