Chapter PS, Problem 1.1P

To determine

To find:

1. The pattern and the next point in positive direction.
2. The next point in negative direction.

Answer to Problem 1.1P

  $y$ coordinate is cube of the $x$ coordinate in both (positive and negative) the directions

  $\begin{array}{l}a.(3,27)\\ b.(-3,-27)\end{array}$

Explanation of Solution

Given:

A function passes through the points as shown:

  

The coordinates given in the graph in positive direction are:

(1, 1) and (2, 8)

The coordinates given in the graph in negative direction are:

(-1, -1) and (-2, -8)

It can be observed that the $y$ coordinate is cube of the $x$ coordinate in both (positive and negative) the directions.

Prediction in positive direction for the next point:

Next $x$ would be 3 and taking its cube to find the $y$ coordinate: $3^3=27$

Prediction in negative direction for the next point:

Next $x$ would be -3 and taking its cube to find the $y$ coordinate: ${(-3)}^3=-27$