Chapter 1.1, Problem 34PPSE

Solution

a.

To identify the pattern followed by the points of the graph given in the problem.

The points of the graph follows the pattern that each point is obtained from the previous one by adding $1$ to the $x$ -coordinate and $3$ to the $y$ -coordinate.

Given the graph:

  

Calculation:

The $x-y$ coordinates of the points represented in the graph are tabulated:

$x$	$y$
$1$	$3$
$2$	$6$
$3$	$9$
$4$	$12$
$5$	$15$

Observe that each point is obtained from the previous one by adding $1$ to the $x$ -coordinate and $3$ to the $y$ -coordinate.

Thus, the points follows the pattern that each point is obtained from the previous one by adding $1$ to the $x$ -coordinate and $3$ to the $y$ -coordinate.

Conclusion:

The points of the graph follows the pattern that each point is obtained from the previous one by adding $1$ to the $x$ -coordinate and $3$ to the $y$ -coordinate.

b.

To determine the outputs of the inputs $6,7,\text{and 8}$ .

The outputs of the inputs $6,7,\text{and 8}$ are $18,21,\text{and}\text{24}$ , respectively.

Calculation:

The last point before the input $6$ :

  $\left(5,15\right)$ .

Then, the next point (corresponding to the input $6$ ) has the coordinates:

  $\left(5+1,15+3\right)=\left(6,18\right)$ .

That is, the output is $18$ when the input is $6$ .

Likewise, the point corresponding to the input $7$ :

  $\left(6+1,18+3\right)=\left(7,21\right)$ .

Proceeding in a similar way, it may be observed that, the output is $24$ when the input is $8$ .

Conclusion:

The outputs of the inputs $6,7,\text{and 8}$ are $18,21,\text{and}\text{24}$ , respectively.