Chapter 4.3, Problem 5STP

For Exercises $1-5,$ choose the correct letter.

Which ordered pair represents a nonlinear function?

A. $(0,0),(1,1),(2,2),(3,3),$ and (4,4)

C. $(0,-1),(1,0),(2,1),(3,2),$ and (4,3)

B. $(0,0),(1,-1),(2,-2),$ and (4,-4)

D. $(0,0),(1,1),(2,8),(3,27),$ and (4,64)

To determine

Write the ordered pair which represents a nonlinear function.

Answer to Problem 5STP

The ordered pair $D. \left(0,0\right),\left(1,1\right),\left(2,9\right),\left(3,27\right)\text{ and }\left(4.64\right)$ represents the nonlinear function, so option (D) is correct.

Explanation of Solution

Given information: The given ordered pairs in options are,

  $\begin{array}{l}A. \left(0,0\right),\left(1,1\right),\left(2,2\right),\left(3,3\right)\text{ and }\left(4.4\right)\\ B. \left(0,0\right),\left(1,-1\right),\left(2,-2\right)\text{ and }\left(4.-4\right)\\ C. \left(0,-1\right),\left(1,0\right),\left(2,1\right),\left(3,2\right)\text{ and }\left(4.3\right)\\ D. \left(0,0\right),\left(1,1\right),\left(2,9\right),\left(3,27\right)\text{ and }\left(4.64\right)\end{array}$

Calculation: The option $D.$ represents the nonlinear ordered pair because its graph is non linear, whose graph is $\left(y=x^3\right)$ whereas the graph for options $A,B\text{and }C$ is linear. Hence option (D) is correct