Chapter 9.1, Problem 30HP

(a)

To determine

To find: The value that is added to each term in the sequence.

Answer to Problem 30HP

The value that is added to each term in the sequenceis $-3$ .

Explanation of Solution

Given information:

The following table:

Calculation:

Since the value added to each term is constant, the value can be found by subtracting any term in the sequence from its next term as follows:

  $33-36=-3$

Hence, $-3$ is added to each term in the sequence.

(b)

To determine

To complete: The given table. Also, explain if the set of ordered pairs a function.

Answer to Problem 30HP

The value that is added to each term in the sequenceis $-3$ .

Explanation of Solution

Given information:

The following table:

Calculation:

Since each term can be obtained by adding $-3$ to the previous term, the table can be completed as follows:

The set of ordered pairs can be written as:

  $\left\{\left(1,36\right),\left(2,33\right),\left(3,30\right),\left(4,27\right),\left(5,24\right),\left(6,21\right),\left(7,18\right)\right\}$

This set of ordered pairs is a function because each domain value is paired with exactly one range value.

(c)

To determine

To graph: The set of ordered pairs. Also, explain the relationship between term number and term shown in the graph.

Explanation of Solution

Given information:

The following table:

Calculation:

The graph of the ordered pairs can be obtained as follows:

Interpretation:

As the term number ( x ) increases, the term value ( y ) decreases.