Chapter 3, Problem 8RE

To determine

Given function is linear or non linear.

Answer to Problem 8RE

Given function is nonlinear.

Explanation of Solution

Given information:

$x$	$y=g\left(x\right)$
$-1$	$-3$
$0$	$4$
$1$	$7$
$2$	$6$
$3$	$1$

Calculation:

To find given function is linear or non linear.

Initially, we have to subtract from next number to previous number of $x$ and $y$ .

So, $\Delta x$ and $\Delta y$ values are:

  $\begin{array}{l}{x}_2-x_1=0-(-1)=1\\ x_3-x_2=1-0=1\\ x_4-x_3=2-1=1\\ x_5-x_4=3-2=1\end{array}$

And

  $\begin{array}{l}{y}_2-y_1=4-\left(-3\right)=-1\\ y_3-y_2=7-4=3\\ y_4-y_3=6-7=-1\\ y_5-y_4=1-6=-5\end{array}$

Now divide the $\Delta y$ by $\Delta x$ ,

  $\begin{array}{l}\frac{\Delta y_1}{\Delta x_1}=\frac{-1}{1}=-1\\ \frac{\Delta y_2}{\Delta x_2}=\frac{3}{1}=3\end{array}$

So, it is observed that $-1\ne 3$

So given function is nonlinear.