Chapter 6.3, Problem 10E

To determine

To find: the nature of the graph formed by the points, $\left(x,f(x)\right)=\left\{\left(-1,\frac{1}{4}\right),\left(0,\frac{1}{2}\right),(1,1),(2,2),(3,4)\right\}$ . And verify whether it represent linear or exponential function.

Answer to Problem 10E

Given graph representing linear function.

Explanation of Solution

Given information :

Given points $\left(x,f(x)\right)=\left\{\left(-1,\frac{1}{4}\right),\left(0,\frac{1}{2}\right),(1,1),(2,2),(3,4)\right\}$ .

Calculation:

Given points of the graph are, $\left(x,f(x)\right)=\left\{\left(-1,\frac{1}{4}\right),\left(0,\frac{1}{2}\right),(1,1),(2,2),(3,4)\right\}$ .

Therefore the difference is,

  $\frac{1}{2}-\frac{1}{4}=\frac{1}{4},1-\frac{1}{2}=\frac{1}{2},2-1=1,4-2=2$

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

Further the common ratio is,

  $\frac{1/2}{1/4}=2,\frac{1}{1/2}=2,\frac{2}{1}=2,\frac{4}{2}=2$

Hence there exist a common ratio $2$ . Therefore the graph will represent a exponential function.

Graph: