Q9. - Algebra 1

Question

SCHOOL ENROLLMENT The table shows the total enrollment in U.S. public schools.

School year	2004-04	2005-06	2006-07	2007-08
Enrollment (in thousands)	48,560	48,710	48,948	49,091

a. Write a set of ordered pairs representing the data in the table if $x$ is the number of school years from 2004-2005

b. Draw a graph showing the relationship between the year and enrollment.

c. Describe the domain and range of the data.

Step-by-Step Solution

Answer

a. The set of ordered pairs representing the data in the given table are $\left(1,48,560\right),\left(2,48,710\right),\left(3,48,948\right),\left(4,49,091\right)$.

b. The graph showing the relationship between the year and the enrollment is as follows:

 

c. The domain of the data is the set $\left\{1,2,3,4\right\}$ and the rage of the data is $\left\{48560,48710,48948,49091\right\}$.

Part a. Step 1. Given.

We are given that,

School year	2004-05	2005-06	2006-07	2007-08
Enrollment (in thousands)	48,560	48,710	48,948	49,091

Part a. Step 2. Calculations.

The number of school years up to 2004-05 is $x=1$.

The number of school years up to 2005-06 is $x=2$.

The number of school years up to 2006-07 is $x=3$.

The number of school years up to 2007-08is $x=4$.

The set of ordered pairs representing the given data is, $\left\{\left(1,48,560\right),\left(2,48,710\right),\left(3,48,948\right),\left(4,49,091\right)\right\}$.

Part a. Step 3. Conclusion.

In conclusion we obtain a set of ordered pair representing the relation between the data in the given table.

Part b. Step 1. Given.

The given information is as in the table,

School year	2004-05	2005-06	2006-07	2007-08
Enrollment (in thousands)	48,560	48,710	48,948	49,091

Part b. Step 2. Calculation.

Figure (1) is the graph showing the relation between the school year and enrollment.

Part b. Step 3. Conclusion.

Taking the given information in the table we draw a graph with the school year along the $x$ axis and the enrollment along the $y$ axis.

Part c. Step 1. Given.

The following is the given information.

School year	2004-05	2005-06	2006-07	2007-08
Enrollment (in thousands)	48,560	48,710	48,948	49,091

Part c. Step 2. Calculation.

The $x$ value of the function will be the domain and $y$ values will be the range of the given data.

Thus the domain of the data is $\left\{1,2,3,4\right\}$ and the rage is $\left\{48560,48710,48948,49091\right\}$.

Part c. Step 3. Conclusion.

The domain of a function is the $x$ component of the function. Thus we obtain the domain. Also for the range we take the $y$ component and obtain the range.