Unit+5+Virtual+Notebook+(Christmas)

===The following assignments are aligned with the lessons we have learned in class. We will be having the test the week we come back from break so this is an excellent chance for you to review so you do not forget the material. Please do not put off all of the assignments until the last minute. All four assignment will be do Monday January 1st by midnight. Happy holidays! ===

In Unit 5 Lesson 4, we learned about inverses and graphing logarithmic. To review topic answer the following questions: __**Part 1**__ Given the function g(x) = x^2 - 7 when x<=0 1.) Find the inverse algebraically and explain your step-by-step process verbally.
 * __Unit 5 Lesson 4__**

2.)The graph of g(x) is labeled below. Explain how you can find at least 4 coordinate points that represent the inverse function. Write the coordinate points you found. I would find 4 points on the original graph below, (0,-7) (-1,-6) (-3,2) and (-4,9) and the inverse of them would be (-7,0) (-6,-1) (2,-3) and (9,-4)

3.) Explain why g(x) was given the domain x<=0 rather than sketching the function when finding the inverse graphically. The inverse's domain is (-3,0] and it's range is (-∞, ∞), while g(x) domain is all real and it's range would possibly be (-3,∞]

4.) Given the domain of a function h(x) is [-3, infinity) and the range is [0,infinity), find domain and range of the inverse function. Explain how you arrived at your answer. The domain of the inverse function would be domain = [0, ∞) and the range would [-3, ∞) because it swaps

1.) Explain the step by step process of graphing the function g(x) = 1 - 2log3(x+4) (this is a log base 3, the 3 should not be distributed through the parenthesis) without using the graphing calculator. Find three point of the function and the three corresponding points of g(x). List the asymptote(s), domain, and range.  2) Explain how you can find the domain and range of any logarithmic function without looking at the graph or using a graphing calculator. Without looking at a graph or using a graphing calculator you can switch the domain and range of the inverse of the function
 * __Part 2__**

In unit 5 lesson 5 we evaluated logarithmic and exponential expressions without using a calculator. Evaluate the following expression. Since I cannot control whether you use a calculator at home you must write your steps out verbally so I know you understand the process.
 * __Unit 5 Lesson 5 __**

In Unit 5 Lesson 6 We learned about rewriting logarithmic expressions by expanding to have multiple logarithms and condensing to have a single logarithm. I want you to prove algebraically, why the following statements are true using properties of logarithms. After break we will be learning how to solve various logarithmic equations and how to do applications algebraically; however if you understand the concept of exponential applications your should be able to solve and analyze a logarithmic application.
 * __Unit 5 Lesson 6__**
 * __Unit 5 Lesson 7__**