Chapter 3, Problem 7RE

To determine

Given function is linear or non linear.

Answer to Problem 7RE

Given function is nonlinear.

Explanation of Solution

Given information:

$x$	$y=f\left(x\right)$
$-1$	$-2$
$0$	$3$
$1$	$8$
$2$	$13$
$3$	$18$

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

  $\begin{array}{l}{y}_2-y_1=3-\left(-2\right)=-1\\ y_3-y_2=8-3=5\\ y_4-y_3=13-8=5\\ y_5-y_4=18-13=5\end{array}$

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

  $\begin{array}{l}\frac{\Delta y_1}{\Delta x_1}=\frac{-1}{1}=-1\\ \frac{\Delta y_2}{\Delta x_2}=\frac{5}{1}=5\end{array}$

So, it is observed that $-1\ne 5$

So given function is nonlinear.