Chapter 1.7, Problem 6LC

a)

To determine

To find:

A set of ordered pairs representing table data in ordered pair form $(x,y)$ .

Answer to Problem 6LC

Required ordered pairs in form $(x,y)$ are;

  $\left(2012,49771\right),\left(2013,50044\right),\left(2014,50132\right),(2015,50268)$

Explanation of Solution

Given information:

Table given below shows the total enrollment in U.S. public school.

  

Also, x represents school years, 2012-13 onwards and y is the total enrollment

Concept used:

While forming an ordered pair, independent variable is put as first number and dependent variable is put as second number. Further the set of all first values of ordered pair is domain and set of all second numbers is range and if for a relation to be a function, each value of its domain must have a unique value in its co-domain.

Calculation:

Values of x will be taken as 2012, 2013, 2014, 2015 as number of school years, so its related ordered pairs will be $\left(2012,49771\right),\left(2013,50044\right),\left(2014,50132\right),(2015,50268)$ .

Conclusion:

So, above data in ordered pair form (Year, Enrollment) can be written as:

  $\left(2012,49771\right),\left(2013,50044\right),\left(2014,50132\right),(2015,50268)$

b)

To determine

To draw:

The related graph between year and enrollment.

Answer to Problem 6LC

Graph representing the relation between year and enrollment is,

  

Explanation of Solution

Given information:

Table given below shows the total enrollment in M public school.

  

Also, , x represents school years, 2012-13 onwards and y is the total enrollment

Concept used:

While forming an ordered pair, independent variable is put as first number and dependent variable is put as second number. Further the set of all first values of ordered pair is domain and set of all second numbers is range and if for a relation to be a function, each value of its domain must have a unique value in its co-domain.

Calculation:

Years will be shown on x axis and enrollment on y axis, while plotting these pairs in XY plane as shown above.

Conclusion:

So, points calculated in ordered pair form, when plotted in XY plane, give the graph as shown above.

c)

To determine

To find:

Domain and range of the data.

Answer to Problem 6LC

Domain is $\{2012,2013,2014,2015\}$ and range is $\{49771,50044,50132,50268\}$ and yes, it is a function.

Explanation of Solution

Given information:

Table given below shows the total enrollment in M public school.

  

Also, , x represents school years, 2012-13 onwards and y is the total enrollment

Concept used:

While forming an ordered pair, independent variable is put as first number and dependent variable is put as second number. Further the set of all first values of ordered pair is domain and set of all second numbers is range and if for a relation to be a function, each value of its domain must have a unique value in its co-domain.

Calculation:

As domain is the set of all first numbers of all ordered pairs, so its domain of given relation is $\{2012,2013,2014,2015\}$ and accordingly as a set of all second numbers of these ordered pairs, range is $\{49771,50044,50132,50268\}$ .

And as for each new first value, there is associated a unique second value in all ordered pairs. So, this relation is surely a function.

Conclusion:

So, as above relation, for each different first value, there is always a unique second value in its given ordered pairs. So, it is surely a function, based on definition of the function.