Chapter 1.7, Problem 6IP

To determine

The domain and range of the relation.

Answer to Problem 6IP

The final table is

Yesterday’s Attendance	Today’s Attendance
X	Y
14	3
18	5
22	7
26	9

Explanation of Solution

Given:

Today’s attendance is 4 less than half of yesterday’s attendance $y=\frac{x}{2}-4$

  

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve the given table. Here to solve the table and simplify as shown below,

  $\begin{array}{c}y=\frac{x}{2}-4\\ x=14\\ \text{Then}y=\frac{x}{2}-4\\ y=\frac{14}{2}-4\\ y=7-4\\ y=3\\ x=18\\ \text{Then}y=\frac{x}{2}-4\\ y=\frac{18}{2}-4\\ y=9-4\\ y=5\\ x=22\\ \text{Then}y=\frac{x}{2}-4\\ y=\frac{22}{2}-4\\ y=11-4\\ y=7\\ x=26\\ \text{Then}y=\frac{x}{2}-4\\ y=\frac{26}{2}-4\\ y=13-4\\ y=9\end{array}$

Thus, the final table is below.

Yesterday’s Attendance	Today’s Attendance
X	Y
14	3
18	5
22	7
26	9