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
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)
The x and y values 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.
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)
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
(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 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 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)
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)
The x and y values 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.
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)
(-3, 1)
(-1, -1)
(5, -3)
VA: x=4
Domain: (-4, Infinity )
Range: ( -Infinity, +Infinity )
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.
(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 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.