Unit+I+Virtual+Notebook+Responses

Unit 1

Lesson 1:
Similarities: They all have to include regular numbers, no fractions or decimals. Differences: Natural numbers do not include zero & integers can be either negative or postive which natural and whole numbers can not be. Rational numbers are apart of the real number system and can be fractions, decimals, along with negative & positive whole numbers while irrational numbers go on forever, and are never true. The reciprocal of a postive real number does not necessarily have to be less then one because a real number can be less than one, such 3/8 the reciporcal of 3/8 is 8/3, which is obviously greater than one. True - An integer in decimal form would be a terminating decimal (2.0, 3.0, 4.0)
 * What are the similarities and differences between a natural number, whole number, and integers?**
 * What is the difference between a rational and irrational number?**
 * 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. **
 * True or False: An integer is a rational number. Explain your answer and use an example if necessary. **
 * True or False: A rational number is an integer. Explain your answer and use an example if necessary. **

In most cases this is false, but in situations like a rational number that is positive or negative (non-fractions) or a number over 1, then it is an integer. True because you have to be one or the other. One must be apart of the real number systems (fractions, decimals, positive/negative numbers) while irrational numbers are polar opposites.
 * 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: **


 * A rational number that is terminating (represented in both fraction and decimal form)
 * 1/4; 0.25
 * A rational number that is infinitely repeating (represented in both fraction and decimal form)
 * 1/3 0.333333333333
 * A real number that fits at least 4 categories of the real number system and explain verbally how that number fits in each category
 * 4 is a natural number because it is a positive whole number. It is a whole number because it is a positive whole number including zero. It is an integer because it is a positive or negative, non-fraction number **including** zero and it is a rational number because it is a terminating decimal in decimal form

Lesson 2
Brackets - Closed Circle on graph, Less than or equal to, Greater than or equal to Parenthesis - Open Circle on graph, (Greater than or Less than)
 * What is the difference from using brackets [] and parenthesis in interval notation. How does this notation relate to graphing an inequality?**

Bounded - two limitations of a solution set Unbounded - No more than one limitation
 * What is the difference between a bounded and unbounded interval?**

Because infinity goes on forever and you can't include it within a certain interval.
 * What is the reasoning for only using parenthesis when infinity is included in your interval?**

Bounded: 4<x<12 or x is all real numbers greater than 4 but less than 12 - (4,12) Unbounded: x<7 or x is all real numbers less than 7 (-infinity,7)
 * 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.**

Lesson 3 -Pythagorean Therom -Graphing/Counting spaces when graph -Distance Formula
 * What are three methods you can use to find the distance between two points on the coordinate plane? Explain when it is most convenient to use each method.**

-Pythagorean Therom -Graphing/Counting spaces when graph -Midpoint Formula
 * What are three methods you can use to find the midpoint of two points on a coordinate plane? Explain when it is most convenient to use each method.**

-Distance Formula -Identifying the given infor -Step one in Solving - Writing down the formula -Subsituting the given info -Simplify -FOIL (Expanding) -Combining like terms -Eliminating square root by squaring both sides -Simplify -Subtract on both sides for the equation to equal zero -Factor -Factors shown as solutions -List solutions as points
 * Given the link to the following example, explain in your own words what is going on during each step of the problem.**

Lesson 5
(x-h)^2 + (y-k)^2=r^2
 * What is the standard form equation of a circle with a radius of (0, 0)**

Find the center of the circle when given the two endpoints of the diameter by using the midpoint formula.
 * Explain in words how you can find the center of a circle if you are given the two endpoints of the diameter.**

Find the radius of the circle if given the center and a point of the circle by using the distance formula with using the points given.
 * 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.**

-Circle tangent to the x-axis is to have one point whose y-value is zero. -Circle tangent to the y-axis is to have one point whose x-value is zero.
 * 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?**