Because the rule you write must work for each ordered pair in the given relation, you must use trial and error to do these problems. The steps are more of a general guideline than a list of commands for how to solve these types of problems. Keep this in mind while doing the steps below. Obviously, stop if you find a rule that works for every ordered pair in the relation. This is your answer.

Step 1. Try a rule in which you add or subtract a number from x.

Step 2. Try a rule in which you multiply x by a number.

Step 3. Try a rule in which you mutlply x by a number then add or subtract some number.

Step 4. Try a rule in which you raise x to an exponent.

Step 5. Try a rule in which you raise x to an exponent then add or subtract some number.

Step 6. Try a rule in which you use absolute value.

Examples Done by Mr. Vizza

Directions: Please write a rule for each of the following relations.

{(4,9), (8,17), (0,1), (-4,-7)}

Step 1. To get from 4 to 9, we add 5.

Try y=x+5

This does not work for (8,17); therefore, this is not the rule.

17=8+5

17=13 False

Step 2. To get from 4 to 9 we multiply by 9/4.

Try y=9/4*x

This does not work for (8,17); therefore, this is not the rule.

17=9/4(8)

17=16 False

Step 3. Try to multiply and add or subtract.

Try y=2x+1

9=2(4)+1

9=8+1

9=9

works

17=2(8)+1

17=16+1

17=17

works

1=2(0)+1

1=0+1

1=1

works

-7=2(-4)+1

-7=-7

works

The rule is y=2x+1.

Problems You Should Try

Directions: Please write a rule for each of the following relations of the form y=... .

1. {(2,10), (-8,0), (-2,6)}

2. {(4,16), (-5,-20), (11,44)}

3. {(0,2), (3,11), (-5,-13)}

4. {(3,9), (4,16), (-5,25)}

5. {(11,7), (0,-4), (-8,-12), (101,97)}

6. {(2,7), (3,26), (-2,-9), (0,-1)}

7. {(5,19), (3,11), (8,31)}

8. {(5,5), (6,6), (0,0), (-1,1)}

9. {(10,102),(0,2),(3,32)}

10. {(1/2,1/4), (r,r²), (-10, 100)}

Directions: Please answer the following word problems.

11. A company keeps track of its profits when selling potato chips. When the company sells 10 cases of potato chips, their profit is $22. Similarly when they sell 8 cases, their profit is $18 and when the sell 4 cases they sell their profit is $10. Please write a rule that reflects their profits in this scenario.

12. There is a rule that reflects the relationship between the number of computer chips a company sells and the cost to produce them. Their cost is $3, when they sell 13 computer chips. Their cost is $6, when they sell 25 computer chips. Similarly, when they sell 37 chips their cost is $9. What is the rule that reflects the relationship?

Writing Exercise

Directions: Please write 1-2 paragraphs that thoroughly address the following.

1. What is the trick in question number twelve above? How did you discover it?

2. How much of the process by which we solve these probems is trial and error? How much is methodical? Is the process some combination of both? Is ther any luck involved? Please explain.

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