Unit+1+Virtual+Notebook

__**Unit 1 Lesson 1**__

In your virtual notebook, answer the following questions:

What are the similarities and differences between a natural number, whole number, and integers? The similarities are that they are all positive and contain no decimals. The difference is that integer can also be negative. Natural numbers does not include zero. What is the difference between a rational and irrational number? Rational number can have terminating and repeating decimals and fractions. Irrational numbers do not terminate nor repeat but they are endless decimals. Explain if the reciprocal of a positive real number must be less then one. If this statement if false prove your argument with an example and explanation. The reciprocal of a positive real number is not always less than one. For example, the reciprocal of 2 is 1/2 which is less than one but the reciprocal of 1/2 is 2. Therefore, the statement is wrong. True or False: An integer is a rational number. Explain your answer and use an example if necessary. True. A integer is a rational number since an integer is just whole numbers that are positive and negative. For example, the number 4, it can be interpreted as 4/1. True or False: A rational number is an integer. Explain your answer and use an example if necessary. False. A rational number cannot be an integer since rational numbers can are fractions which are either terminating or repeating decimals. And integer cannot have decimals. True or False: A number is either rational or irrational, but not both. Explain your answer and use an example if necessary. Give an example of a real number set that includes the following elements: True since irrational numbers are never terminating or repeating decimals. It goes on forever like Pi. A rational number that is terminating (represented in both fraction and decimal form) 2.5 or 5/2 A rational number that is infinitely repeating (represented in both fraction and decimal form) 1/9 or 0.1111111111111 A real number that fits at least 4 categories of the real number system and explain verbally how that number fits in each category 10. A natural number is all positive whole numbers that does not include 0. Same with Whole numbers and integers since they are they include 0 and positive numbers. Integers can include negative. It is also a rational number is it can be interpret as 10/1.


 * __ Unit 1 Lesson 2 __**

In your virtual notebook, answer the following questions:

What is the difference from using brackets [] and parenthesis in interval notation. How does this notation relate to graphing an inequality? Brackets are used to show that they are equal to or less/greater than a number. Parenthesis are used to show if the numbers are less or greater than a number. What is the difference between a bounded and unbounded interval? A bounded interval has 2 endpoints that are connected to each other. Unbounded intervals has at least 1 end point but they continue on forever. What is the reasoning for only using parenthesis when infinity is included in your interval? Parenthesis must be used for infinity since the number can never equal to infinity. The number will just keep increasing and never stopping at a specific number in infinity. Give an example of a bounded interval and an unbounded interval. Represent the interval as an inequality and verbal. You may not use an example shown in your reading. A bounded interval would be something like (8,66), or x is greater than 8 but less than 66. An unbounded interval would be (-** ∞ **,6), or x is less than 6.


 * __ Unit 1 Lesson 5 __**

In your virtual notebook, answer the following questions: What is the standard form equation of a circle with a radius of (0, 0) x^2 + y^2 = r^2 Explain in words how you can find the center of a circle if you are given the two endpoints of the diameter. You can use the midpoint formula to find the radius if you have the diameter. Explain in your own words how you can find the radius of a circle if you are given the center and a point on the circle. You can use the distance formula to find the radius. Using another resource, write the mathematical definition of the word tangent in your own words (remember to include the name of the resource you used). Predict what you think it means for a circle to be tangent to the x-axis? Predict what you think it means for a circle to be tangent to the y-axis? You may change your predictions after tomorrows class discussion. Tangent is a line in the plane of a circle that intersects the circle at exactly one point. I think that it means the tangent would be touching the circle from the x-axis and the same with y-axis.