# 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.

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#### Solution Summary

This provides brief examples and explanations for functions and equations and converting standard and metric measurement.

Radical Signs and Advantages of Rational Exponents; Loudness of Sound - Formula and Measurement; Index of a Sequence - Range, Domain, Aritmetic and Geometric Sequences

1. While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational exponents over the radical sign. Include in your answer an example of an equation easier to solve as a rational exponent rather then a radical sign.

2. The loudness of sound is based on intensity level measured in decibels using a logarithmic scale and is relative to (a ratio of) the weakest sound the ear can hear.

Using the Cybrary, web resources, and other course material, research how sound is measured. Include the following items in your posting:

? The formula for measuring sound.

? Pick a specific sound, give the decibels of the sound, and explain what this measurement means.

3. Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function?

Include the following in your answer:

? Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence?

? Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric sequence?

? Give at least two real-life examples of a sequences or series. One example should be arithmetic, and the second should be geometric. Explain how these examples would affect you personally.