Unit+1+Virtual+Homework

__**Unit 1 Lesson 1**__

In your notebook, answer the following questions:
 * Part 1**
 * 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.
 * 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)
 * A rational number that is infinitely repeating (represented in both fraction and decimal form)
 * A real number that fits at least 4 categories of the real number system and explain verbally how that number fits in each category

In your notebook, answer the following questions:
 * Part 2**


 * What is the difference from using brackets [] and parenthesis in interval notation. How does this notation relate to graphing an inequality?
 * What is the difference between a bounded and unbounded interval?
 * What is the reasoning for only using parenthesis when infinity is included in your interval?
 * 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.


 * __ Unit 1 Lesson 2 __**

In your notebook, answer the following questions:


 * 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.
 * 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.
 * Given the link to the following example, explain in your own words what is going on during each step of the problem.



Read and take notes on Solving Equations Graphically, Numerically, and Algebraically on pages 44-49 in your classroom binder. Definitions and steps to problems in your own words should be in the left column and examples and comments should be in the right column.
 * __ Unit 1 Lesson 5 __**


 * What are some of the methods to solve quadratic equations algebraically? Explain when it is more convenient to use each method? What methods can be used in any situation and which method's usage is restricted? Explain.
 * When is a table of values useful to help find solutions to an equation? Explain.
 * In your own words, how can you solve an equation graphically using intersections?
 * Describe why absolute value equations sometimes have two solutions. How can you get the two solutions by solving algebraically.