Chapter 8.1, Problem 39HP

(a)

To determine

To calculate: To find what value was added to each term of the sequence

Answer to Problem 39HP

  $-3$ is added to each term in the sequence

Explanation of Solution

Given information: Sequence is $36,33,30,27,\mathrm{....}$

Formula Used:

Sequence is an arithmetic sequence when the difference between the two terms is constant.

Nth term in arithmetic sequence is given as

  $T_n=a+\left(n-1\right)d$

Where,

  $a=$ first term

  $d=$ common difference

  $n=$ term number

Calculation:

Sequence is given as follows:

  $36,33,30,27,\mathrm{....}$

Let us find the difference between each term

  $\begin{array}{l}33-36=-3\\ 30-33=-3\\ 27-30=-3\end{array}$

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

Conclusion:

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

(b)

To determine

To calculate: To find and explain if the set of ordered pairs (term number, term) is a function

Answer to Problem 39HP

The set of ordered pair (term number, term) is a function

Explanation of Solution

Given information: Sequence is $36,33,30,27,\mathrm{....}$

Formula Used:

According to function rule, no input can have more than one output.

The set ordered pairs is referred to as function when no two ordered pairs have the same first coordinate with different second coordinate

Calculation:

Table is completed as follows:

Term Number	Term
1	36
2	33
3	30
4	27
5	24
6	21
7	18

From above table, Set of ordered pairs (term number, term) is

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

Here, no two ordered pairs have same first coordinate.

Thus, the set of ordered pairs is a function

Conclusion:

Hence, the set of ordered pairs is a function

(c)

To determine

To calculate: To graph the set of ordered pairs

Answer to Problem 39HP

The set of ordered pair (term number, term) is a function

Explanation of Solution

Given information: Sequence is $36,33,30,27,\mathrm{....}$

Formula Used:

According to function rule, no input can have more than one output.

The set ordered pairs is referred to as function when no two ordered pairs have the same first coordinate with different second coordinate

Calculation:

Table is completed as follows:

Term Number	Term
1	36
2	33
3	30
4	27
5	24
6	21
7	18

From above table, Set of ordered pairs (term number, term) is

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

Plotting the points in graph,

  

With every increase in term number, term is decreasing by $3$ units

Conclusion:

Hence, the graph is sketched