Unit+1+Virtual+Notebook

__**Unit 1 Lesson 1**__ >> Whole numbers are positive whole numbers that contain 0. >> Integers include positive/negative numbers and include 0. >> Ex: 3 -> 3/1 -> 1/3 -> less than 1 >> Ex. 39 -> 1/39 -> less than 1
 * What are the similarities and differences between a natural number, whole number, and integers?
 * Natural numbers contains all postive whole numbers, but deos not included 0.
 * What is the difference between a rational and irrational number?
 * Rational - Fractions, Whole numbers, Negatives, Terminating decimals, Repeating decimals
 * Irrational - No Terminating decimals, No repeating 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 the positive number is always less than one because a positive number is also equaled to the number over a denominator of 1.
 * True or False: An integer is a rational number. Explain your answer and use an example if necessary.
 * True. Integers, etc are sub categories of rational numbers
 * True or False: A rational number is an integer. Explain your answer and use an example if necessary.
 * False. An integer can not have fractions,but a rational number can.
 * True or False: A number is either rational or irrational, but not both. Explain your answer and use an example if necessary.
 * True. A number can not apply to both rational and irrational because of different rules.
 * 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)
 * 3/4 or 0.75
 * A rational number that is infinitely repeating(represented in both fraction and decimal form)
 * 1/6 or 0.666...
 * A real number that fits at least 4 categories of the real number system and explain verbally how that number fits in each category
 * 3 because its not 0 [Natural], positive/no fractions [Whole], positive/no fractions [Integer], whole number/non terminating [Rational]

**__Unit 1 Lesson 2__**
 * What is the difference from using brackets [] and parenthesis in interval notation. How does this notation relate to graphing an inequality?
 * [ ]= included/closed circle, = not included/close circle
 * The notation relates because it decides which way the arrow points to, if it's greater/less/equal to and whether the circle is opened/closed
 * What is the difference between a bounded and unbounded interval?
 * Bounded: Defined endpoint, no positive/negative infinity
 * Unbounded: No endpoints, go to positive/negative infinity
 * What is the reasoning for only using parenthesis when infinity is included in your interval?
 * Infinity does not have an exact endpoint, meaning it's unbounded and goes on forever
 * 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.
 * (3,9] || x is less than 3 but greater than or equal to 9 || 3 < x __<__ 9
 * ======(- ∞,3) || x is less than 3 || -∞ < x < 3======

**__Unit 1 Lesson 5__** >>
 * What is the standard form equation of a circle with a radius of (0, 0)
 * r//² =// (x − h)//²// + (y − k)//²//
 * Explain in words how you can find the center of a circle if you are given the two endpoints of the diameter.
 * Using the distance formula to find the distance of the two endpoints and finding the midpoint afterwards which would be the center.
 * 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.
 * Plug given information into the standard form equation of a circle formula and solve.
 * 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 predicitions after tomorrows class discussion.
 * A tangent is a line that touches the circle at one side and is solved by the equation ////tan(x) = (opposite side / adjacent side).//// I think for a circle to be tangent to the x-axis, the radius is perpendicular to the x-axis and vise versa for the y axis.
 * []