Chapter 1.6, Problem 20HP

a.

To determine

To explain:The data represented in the complete table is a function or not.

  $\begin{array}{cc}x& y\\ 1& 1\\ 4& \\ 9& \\ 16& \\ & 5\\ 36& \end{array}$

Answer to Problem 20HP

The complete table is provided below,

  $\begin{array}{cc}x& y\\ 1& 1\\ 4& 2\\ 9& 3\\ 16& 4\\ 25& 5\\ 36& 6\end{array}$

The data in the table represents the function.

Explanation of Solution

Given information:

The table,

  $\begin{array}{cc}x& y\\ 1& 1\\ 4& \\ 9& \\ 16& \\ & 5\\ 36& \end{array}$

Formula used:

A relation is said to be a function if every element of domain is mapped to exactly one element of range.

Calculation:

Consider the table,

  $\begin{array}{cc}x& y\\ 1& 1\\ 4& \\ 9& \\ 16& \\ & 5\\ 36& \end{array}$

Here the x represent the number that is square of a whole number.

And y represent the positive square root of the number x .

So, square root of 4 is 2, 9 is 3, 16 is 4 and 36 is 6.

Also square of 5 is 25. Therefore, complete table is.

  $\begin{array}{cc}x& y\\ 1& 1\\ 4& 2\\ 9& 3\\ 16& 4\\ 25& 5\\ 36& 6\end{array}$

Recall that relation is said to be a function if every element of domain is mapped to exactly one element of range.

The elements of domain are $\left\{1,4,9,16,25,36\right\}$ and elements of range are $\left\{1,2,3,4,5,6\right\}$ .

Each member of domain is mapped to exactly one element of range. Therefore, it represent a function.

b.

To determine

To graph: The scatter plot between square of whole numbers and its positive square root.

Explanation of Solution

Given information:

The data is provided below.

  $\begin{array}{cc}x& y\\ 1& 1\\ 4& 2\\ 9& 3\\ 16& 4\\ 25& 5\\ 36& 6\end{array}$

Graph:

When the relationship between two data sets is to be analyzed scatter plot is used.

Provided two data sets. Here the x represent the number that is square of a whole number.

And y represent the positive square root of the number x .

  $\begin{array}{cc}x& y\\ 1& 1\\ 4& 2\\ 9& 3\\ 16& 4\\ 25& 5\\ 36& 6\end{array}$

On the x -axis of coordinate plane denote the number from 1 to 40.

On y -axis plot denote the number from 1 to 6.

The scatter plot of the data is provided below,

  

Interpretation:

It is observed as the square of whole number increases its square root value also increases that is there is a strong positive linear relationship between x and y .

c.

To determine

To explain:The data represented in the complete table when the x and y coordinates are revered is a function or not.

  $\begin{array}{cc}x& y\\ 1& 1\\ 4& \\ 9& \\ 16& \\ & 5\\ 36& \end{array}$

Answer to Problem 20HP

The complete table is provided below,

  $\begin{array}{cc}x& y\\ 1& 1\\ 2& 4\\ 3& 9\\ 4& 16\\ 5& 25\\ 6& 36\end{array}$

The data in the table represents the function.

Explanation of Solution

Given information:

The table,

  $\begin{array}{cc}x& y\\ 1& 1\\ 4& \\ 9& \\ 16& \\ & 5\\ 36& \end{array}$

Formula used:

A relation is said to be a function if every element of domain is mapped to exactly one element of range.

Calculation:

Consider the table,

  $\begin{array}{cc}x& y\\ 1& 1\\ 4& \\ 9& \\ 16& \\ & 5\\ 36& \end{array}$

Here the x represent the number that is square of a whole number.

And y represent the positive square root of the number x .

Now, reverse the x and y coordinates.

So, square root of 4 is 2, 9 is 3, 16 is 4 and 36 is 6.

Also square of 5 is 25. Therefore, complete table is.

  $\begin{array}{cc}x& y\\ 1& 1\\ 2& 4\\ 3& 9\\ 4& 16\\ 5& 25\\ 6& 36\end{array}$

Recall that relation is said to be a function if every element of domain is mapped to exactly one element of range.

The elements of domain are $\left\{1,2,3,4,5,6\right\}$ and elements of range are $\left\{1,4,9,16,25,36\right\}$ .

Each member of domain is mapped to exactly one element of range. Therefore, it represent a function.

d.

To determine

To graph: The scatter plot between whole number and square value of the whole number.

Explanation of Solution

Given information:

The data is provided below.

  $\begin{array}{cc}x& y\\ 1& 1\\ 2& 4\\ 3& 9\\ 4& 16\\ 5& 25\\ 6& 36\end{array}$

Graph:

When the relationship between two data sets is to be analyzed scatter plot is used.

Provided two data sets. Here the x represent the whole number.

And y represent the square value of the number x .

  $\begin{array}{cc}x& y\\ 1& 1\\ 2& 4\\ 3& 9\\ 4& 16\\ 5& 25\\ 6& 36\end{array}$

On the x -axis of coordinate plane denote the number from 1 to 6.

On y -axis plot denote the number from 1 to 40.

The scatter plot of the data is provided below,

  

Interpretation:

It is observed as the whole number increases its square value also increases that is there is a strong positive linear relationship between x and y .