Functions and equations and measurement

This Discussion Question will concentrate on functions and graphs. Understanding the definitions of words is the essence of mathematics. When we understand the meaning of words, finding a solution is much easier because we know what task the problem is asking us to complete.

a. Part 1

b. In your own words, define the word "function."

c. Give your own example of a function using a set of at least 4 ordered pairs. The DOMAIN will be any four integers between 0 and +10. The RANGE will be any four integers between -12 and 5. Your example should NOT be the same as those of other students or the textbook. There are thousands of examples.

e. Explain why your example models a function. This is extremely important for your learning.

f. Give your own example of at least 4 ordered pairs that DOES NOT model a function. The DOMAIN will be any four integers between 0 and +10. The RANGE will be any four integers between -12 and +5. Your example should NOT be the same as those of other students or the textbook. There are thousands of examples.

g. Explain why your example DOES NOT model a function.

Part 2

a. Select any two integers between -12 and +12 which will become solutions to a system of two equations.

b. Write TWO EQUATIONS that have your two integers as solutions. Your solution and equations should NOT be the same as those of other students or the textbook. There are infinite possibilities.

c. Solve your system of equations by the Addition/Subtraction method. Make sure you show the necessary 5 steps. Use the example on Page 357 of your textbook as a guide.

Week Three Discussion 2

This Discussion tests our ability to use a ruler and convert from Standard English measure to Metrics. Students will then apply their knowledge of the geometric measurements of area and volume through real world problems.

a. Choose a room in your house. Measure the length, the width and the height. Make sure you use feet and inches. Most rooms are not a whole number such as 10 feet; they are 10 feet and 3 inches, or 9 feet 6 inches, etc.

b. Record your dimensions and using the appropriate formula find the surface area of the room.

c. A gallon of paint covers about 350 square feet. How many gallons would be required to paint the room? Round up to the nearest gallon.

d. If a gallon of paint costs $22.95 plus 8% tax, what would be the total cost to paint the room?

e. One inch is equivalent to 2.54 centimeters. Convert your English measurements to metrics. Record each dimension in centimeters. Show your conversions.

f. Find the volume in cubic centimeters. Be neat and precise.

g. If each dimension (length, width and height) is doubled, what happens to the volume of the room? Show your work.