Recent Changes

Domain of h(x): [0, infinity)
Range of h(x): [-3,infinity)
I arrived at this answer due to the fact that when creating an inverse function, the 'x'The x and 'y'y values change.always switch
Part 2
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 parent function and the three corresponding points of g(x). List the asymptote(s), domain, and range.
1 unit
-
- Create a inverse function
(-1,1/3)
(0,1)
(1,3)
(2,9)
y values
(1/3,-1)
(1/3,-1)
(1,0)
(3,1)
(9,2)
2/3, 3) > VA :
(-3, 1)
(-1, -1)
(5, -3)
VA: x=4
(-3, 1) Domain: ( -4,
Domain: (-4, Infinity )
(-1, -1) Range:
Range: ( -Infinity, +Infinity )
(5, -3)
2.) Explain how you can find the domain and range of any logarithmic function without looking at the graph or using a graphing calculator.
+Infinity ).
Unit 5 Lesson 5
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 4
In Unit 5 Lesson 4, we learned about inverses and graphing logarithmic functions. To review this 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.
g(x) = x^2 - 7
y = x^2 - 7
x = y^2 - 7
x + 7 = y^2
squareroot(x+7) = y
g(x)^-1 =squareroot(x+7)
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.
(0,-7), (-1,-6), (-3,2), (-4,9)
Switch the x and y values to find coordinate points that represent the inverse function.
(-7,0), (-6,-1), (2,-3), (9,-4)
{Unit_5_Lesson_4_Journal.png} Unit_5_Lesson_4_Journal.png
3.) Explain why g(x) was given the domain x<=0 rather than sketching the entire function when finding the inverse graphically.
The g(x) was given the domain of x<=0 rather than sketching the entire function when finding the inverse graphically because it shows where x is less than or equal to 0 because the range would have a max of y<=0 because the x and y values switch (when you find the inverse).
4.) Given the domain of a function h(x) is [-3, infinity) and the range is [0, infinity), find the domain and range of the inverse function. Explain how you arrived at your answer.
Domain of h(x): [0, infinity)
Range of h(x): [-3,infinity)
I arrived at this answer due to the fact that when creating an inverse function, the 'x' and 'y' values change.
Part 2
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 parent function and the three corresponding points of g(x). List the asymptote(s), domain, and range.
Left 4, stretch 2, up 1 unit
- Create a table of the inverse function
(-1,1/3)
(0,1)
(1,3)
(2,9)
- Switch x and y values
(1/3,-1)
(1,0)
(3,1)
(9,2)
(-3 2/3, 3) > VA : x=4
(-3, 1) Domain: ( -4, Infinity )
(-1, -1) Range: ( -Infinity, +Infinity )
(5, -3)
2.) Explain how you can find the domain and range of any logarithmic function without looking at the graph or using a graphing calculator.
To find the domain, you have to set everything inside parenthesis to >0 and the range will always be ( -Infinity, +Infinity ).
Unit 5 Lesson 5
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_Journal.png} Unit_5_Lesson_5_Journal.png
(A) Change the denominator into e^(2/5).
Ln and e cancel each other out.
1/(2/5) is left, which is (5/2).
(B)
(C) Bring the 3 to the front as a coefficient.
Log base2 16 is 4, because 2^(4) is 16
3 times 4 is 12.
(D) Bring both the 2 and the 3 out front as coefficients
Cross out ln and e. 2 - 3 is -1.
(E) change the fraction into 16^-1.
Bring the -1 to the front as a coefficient.
Log base4 16 is 2 ( 4^(2) is 16 )
-1 times 2 is -2.
(F)
Unit 5 Lesson 6
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.
{Unit_5_Lesson_6_Journal.png} Unit_5_Lesson_6_Journal.png
Unit 5 Lesson 7
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_7_Journal.png} Unit_5_Lesson_7_Journal.png

2. True or false: A rational function as a vertical asymptote at x = c every time c is a zero of the denominator. If the statement is false justify your answer using mathematical terminology learned in class and examples of at least 2 functions that make this statement false.
True
3. Describe how the graph of a nonzero rational function f(x) = (ax+b)/(cx+d) can be obtained from the graph y = 1/x.
You can determine the y-int, x-int, the vertical asymptote, and horizontal asymptote. The graph is shifted left ax = -b units and down cx = -d units. The y-int is b/d. For the x-int, you cross multiply, where the denominator is canceled out, and you solve 0 = ax + b.
4. Write a rational function with the following properties:
Unit 4 Lesson 2--(a) Vertical asymptotes: x = -5 and x = 2.(a) Vertical asymptotes: x = -5 and x = 2
1/x2+3x-10
Unit 4 Lesson 2--(b) Horizontal asymptote: y = -3.(b) Horizontal asymptote: y = -3
(1/x2-9) -3
Unit 4 Lesson 2--(c) y-intercept 1.(c) y-intercept 1
1/x+1

Unit 2
Unit 3 Lesson 5
Solve the following problems on a separate piece of paper. Use your solutions to answer the following summary questions in your virtual notebook.
Example 1:
a.) (x+2)(4x^2 - 17x +37) + (-84)
b.) 4(-2)^3 - 9(-2)^2 + 3(-2) -10 = -84

f(x) = 4x^3 - 9x^2 + 3x -10 g(x) = x + 2
b.) Find f(-2) when f(x) = 4x^3 - 9x^2 + 3x -10
Summary Questions
1. What do you notice about your solutions in part a and part b. In your explanation include what you got for solution to parts a and b to support your explanation.
2. How can what you found be used as a short cut method to see if a number is a zero of a polynomial function or if a binomial is a factor before starting the synthetic division process? Explain.
3. Look up the definition of the remainder theorem and factor theorem on page 215 and 216 of your text. Explain what these theorems mean in your own words using the examples above. Are there any restrictions to using the remainder theorem? Explain.
4. Explain when polynomial division is the appropriate method to use when dividing two polynomials. Explain when synthetic division is the most appropriate method to be used. Can you divide f(x) = 4x^3Answers:
Example 1:
a.) (x+3)(x^2 - 8x^24x + 2x14) + (-43)
b.) (-3)^3 - (-3)^2 + 2(-3) - 1 by g(x) = 2x-43
Example 2:
a.) (x-2)(2x^2 + 1 using synthetic division? If you can explain what you would use as your k value.x +6) + (5)
b.) 2(2)^3 - 3(2)^2 + 4(2) - 7 = 5
Example 3:
a.) (x+2)(4x^2 - 17x +37) + (-84)
b.) 4(-2)^3 - 9(-2)^2 + 3(-2) -10 = -84

Unit 2 Lesson 5
Solve the following problems on a separate piece of paper. Use your solutions to answer the following summary questions in your virtual notebook.
Example 1:
a.) Divide f(x) by g(x) using synthetic or polynomial division.
f(x) = x^3 - x^2 + 2x -1 g(x) = x + 3
b.) Find f(-3) when f(x) = x^3 - x^2 + 2x -1
Example 2:
a.) Divide f(x) by g(x) using synthetic or polynomial division.
f(x) = 2x^3 - 3x^2 + 4x -7 g(x) = x - 2
b.) Find f(2) when f(x) = 2x^3 - 3x^2 + 4x - 7
Example 3:
a.) Divide f(x) by g(x) using synthetic or polynomial division.
f(x) = 4x^3 - 9x^2 + 3x -10 g(x) = x + 2
b.) Find f(-2) when f(x) = 4x^3 - 9x^2 + 3x -10
Summary Questions
1. What do you notice about your solutions in part a and part b. In your explanation include what you got for solution to parts a and b to support your explanation.
2. How can what you found be used as a short cut method to see if a number is a zero of a polynomial function or if a binomial is a factor before starting the synthetic division process? Explain.
3. Look up the definition of the remainder theorem and factor theorem on page 215 and 216 of your text. Explain what these theorems mean in your own words using the examples above. Are there any restrictions to using the remainder theorem? Explain.
4. Explain when polynomial division is the appropriate method to use when dividing two polynomials. Explain when synthetic division is the most appropriate method to be used. Can you divide f(x) = 4x^3 - 8x^2 + 2x - 1 by g(x) = 2x + 1 using synthetic division? If you can explain what you would use as your k value.

1. In your own words, write the steps of performing a graphical transformation. Include any key reminders you think a students will forget in your description.
2. The graph of a function f(x) is illustrated. Use the graph of f(x) to perform the following graphical transformations. You do not need to show the shifted graph, you just need to list the 6 corresponding points. Answer each part seperately.
{http://sarah.chasetower.com/graph_transformation1_worksheet_files/image002.jpg} external image image002.jpg
(a) H(x) = f(x + 1) -2 (left 1 and down 2 units)
(b) Q(x) = 2f(x) (stretched by 2)
(c) P(x) = -f(x) (reflection over x-axis)
3. Suppose that the x-intercepts of the graph of f(x) are -5 and 3. Explain your thinking process or what helped you arrive at your answers.
(a) What are x-intercepts if y = f(x+2)? (shifted to the left two units)
(b) What are x-intercepts if y = f(x-2)? (shifted to the right two units)
(c) What are x-intercepts if y = 4f(x)? (stretched vertically by 4)
(d) What are x-intercepts if y = f(-x)? (reflected over the y-axis)
4. Suppose that the function f(x) is increasing on the interval (-1, 5). Explain your thinking process or what helped you arrive at your answers.
(a) Over which interval is the graph of y = f(x+2) increasing? (left 2 units)
(b) Over which interval is the graph of y = f(x-5) increasing? (right 5 units)
(c) Over which interval is the graph of y = f(x)-1 increasing? (down 1 unit)
(d) Over which interval is the graph of y = -f(x) increasing? (reflected over x-axis)
(e) Over which interval is the graph of y = f(-x) increasing? (reflected over y-axis)

Unit 2 Lesson 3
The following graphs represent even and odd functions. I sorted the functions for you according to whether the function is an even function or an odd function.
Even Functions
{http://image.tutorvista.com/Qimages/QD/16658.gif} external image 16658.gif
Odd Functions
{http://library.thinkquest.org/2647/media/oddxxx.gif} external image oddxxx.gif {http://www.mathwords.com/o/o_assets/o13.gif} external image o13.gif {http://demo.activemath.org/ActiveMath2/LeAM_calculusPics/OddFunction.png?lang=en} external image OddFunction.png?lang=en
In your virtual notebook answer the following questions:
Based on the classifications, when given a graphical representation what do you observe about all of the even functions?
Based on the classifications, when given a graphical representation what do you observe about all of the odd functions?
Do you think a function always has to be odd or even? Explain. Support your answer with an example if necessary.
How can you tell if a function is even or odd looking at a table of values? Explain.
How can you prove a function is even or odd algebraically? What steps should you take to prove whether a function is even of odd algebraically using the definition? Explain.
1. The graph is symmetrical about the y-axis.
2. The graph is symmetrical about the origin.
3. No, because not all graphs are symmetrical to either of the axis like an even and odd function.
4. If the y values are the same with same signs, then it's even. If the y-values are the same but with opposite signs, then it's an odd function.
5. For all x in the domain of f, f(-x) = f(x). This is when you plug in -x for all the in the function. Functions with this property are even.
For all x in the domain of f, f(-x) = -f(x). This means the entire function is negative and not just the x values. These functions are odd.

Look up the mathematical definition for domain and write what domain means in your own words. How do your observations made about each function and table of values relate to this definition? Explain.
What do your think would be an appropriate domain for a function representing the population of deer from the years 1975-2005? Explain.
1. f(x) is a quadratic function, because of the x squared. Plus, when i graph the function, it shapes up to a parabola.
g(x) is a square root function.
h(x) is a logarithmic function,when the polynomial in the denominator is 0 then the rational function becomes infinite or the assymptote in its graph.
2. The f(x) values on the table are the same for both positive and negative number (ex: -5 = 20 - 5 = 20). This is probably because the graph shapes up to make a parabola, and a parabola is symmetrical.
3. I noticed that in the g(x) function, there was a lot of "errors" in the table of contents. That's because the graph has a starting point, and becausethere can't be negative numbers inside a square root.
4. For the last graph, the logarithmic graph, I noticed that there were a lot of decimals for h(x). This is probably because this kind of graph has an assymptote. The graph will never touch, though it will get pretty close, to the assymptote.
5. Domain: The domain of a function is the set of all possible input values (usually x), which allows the function formula to work.
The domain of the function determines the shape of the graph.

What type of function is f(x)? g(x)? and h(x)? Explain.
What observations did you make about the table of values and graph of f(x)?Explain how this relates to the function and why you think this happened.
What observations did you make about the table of values and graph of g(x)? Explain how this relates to the function and why you think this happened.
What observations did you make about the table of values and graph of h(x)? Explain how this relates to the function and why you think this happened.
Look up the mathematical definition for domain and write what domain means in your own words. How do your observations made about each function and table of values relate to this definition? Explain.
What do your think would be an appropriate domain for a function representing the population of deer from the years 1975-2005? Explain.