Chapter 6.3, Problem 12E

To determine

To find: the nature of the graph formed by the points, $\left(x,f(x)\right)=\left\{\left(-1,-1\right),\left(-2,-6\right),(0,-2),(3,1),(2,-2)\right\}$ . And verify whether it represent linear or exponential function.

Answer to Problem 12E

Given graph representing neither linear nor exponential function.

Explanation of Solution

Given information :

Given points $\left(x,f(x)\right)=\left\{\left(-1,-1\right),\left(-2,-6\right),(0,-2),(3,1),(2,-2)\right\}$ .

Calculation:

Given points of the graph are, $\left(x,f(x)\right)=\left\{\left(-1,-1\right),\left(-2,-6\right),(0,-2),(3,1),(2,-2)\right\}$ .

Therefore the difference is,

  $-6-(-1)=-5,-2-(-6)=4,1-(-2)=3,-2-1=-3$

So there is no constant difference between each terms. Hence the graph is not represents a linear function.

Further the common ratio is,

  $\frac{-6}{-1}=6,\frac{-2}{-6}=\frac{1}{3},\frac{1}{-2}=-\frac{1}{2},\frac{-2}{1}=-2$

Hence there exist no common ratio. Therefore the graph will not represent a exponential function.

Hence the graph will not represent linear or exponential graph.

Graph: