Module 1 Transformations
| Site: | Joans-place |
| Course: | Math 30-1 |
| Book: | Module 1 Transformations |
| Printed by: | Guest user |
| Date: | Saturday, 23 November 2024, 5:21 AM |
Description
These are the lessons for the Transformations module
Lesson 1 Horizontal & Vertical Translations
This is a Project Based course.
Here is the link for your project. Scroll down to the bottom of the module. Please check it out before you proceed - it is half of your module grade.
Lesson Questions
- How are the graphs of the functions y = f(x) and y − k = f(x − h) related?
- How can you graph the function y − k = f(x − h) given y = f(x)?
Lesson
Click on Lesson 1 and work through the whole lesson. You can expect this to take about three hours before doing the project work. Remember that the Assignment is for practice and NOT to be handed in.
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Multimedia
Self Check Quiz
Each lesson will have a quiz to help you know how you are doing. You have three chances for each quiz and we count the best score only.
Project work
Lesson 2 Reflections
This is a Project Based course.
Here is the link for your project. Scroll down to the bottom of the module. Please check it out before you proceed - it is half of your module grade.
Lesson Questions
- How is a point related to its reflection?
- How are the graphs of the functions y = f(x), y = f(−x), and y = −f(x) related?
- How can you graph the function y = f(−x) or y = −f(x) given y = f(x)?
Lesson
Click on Lesson 2 and work through the whole lesson. You can expect this to take about three hours before doing the project work. Remember that the Assignment is for practice and NOT to be handed in.
Link to Learn Everywhere lessons
Multimedia
Self Check Quiz
Project work
Lesson 3 Stretches
This is a Project Based course.
Here is the link for your project. Scroll down to the bottom of the module. Please check it out before you proceed - it is half of your module grade.
Lesson Questions
- How are the graphs of the functions y = f(x) and y = af(bx) related?
- How can you graph the function y = af(bx) given y = f(x)?
Lesson
Click on Lesson 3 and work through the whole lesson. You can expect this to take about three hours before doing the project work. Remember that the Assignment is for practice and NOT to be handed in.
Link to Learn Everyware Lessons
Multimedia Activity
Benchmark- Stretches
Benchmark assignments give you a chance to practice to the level required for this section. Detailed solutions are provided.1. The graph of a function y = f(x) is transformed as described below. The equation of it's image has the form y = af(bx). Determine the values of a and b for each transformation.
a) Stretch by a factor of 1/3 horizontally and a factor of 1/2 vertically.
b) Stretch by a factor of 2 horizontally and by a factor of 3 vertically.
c) Stretch by a factor of 1/2 horizontally and expand by a factor of 4 vertically.
d) Stretch by a factor of 4 horizontally and compress by a factor of 1/2 vertically.
Lesson 4 Combinations
This is a Project Based course.
Here is the link for your project. Scroll down to the bottom of the module. Please check it out before you proceed - it is half of your module grade.
Lesson Questions
- How can multiple transformations be applied to a function?
- How can you write the equation of a transformed function given the original graph?
Lesson
Click on Lesson 4 and work through the whole lesson. You can expect this to take about three hours before doing the project work. Remember that the Assignment is for practice and NOT to be handed in.
Link to Learn Everywhere lessons
Math Notes:
Examples of Combined Transformations
Multimedia Activity
A good site for looking at the transformations of functions:
http://www.math.hmc.edu/calculus/tutorials/transformations/
A good site for combined transformations:
http://education.ti.com/html/t3_free_courses/calculus84_online/mod03/mod03_lesson2.html
Self Check Quiz
Each lesson will have a quiz to help you know how you are doing. You have three chances for each quiz and we count the best score only.
Project work
Benchmark - Combinations
Benchmark assignments give you a chance to practice to the level required for this section. Detailed solutions are provided.1. Describe how the graph of each of the following functions can be obtained from the graph of y = f(x). ( 4 marks)
a) y = f(-x + 2)
b) y = f(2x + 8 ) - 4
c) y = f(4 - x) + 5
d) y - 8 = f(3x - 6)
2. The height, y meters, of an emergency flare fired upward from a small boat can be modelled by the function:
y = -5(x - 4)2 + 80
where x seconds is the time since the flare was fired. (4 marks)
a) Describe how the graph of y = -5(x - 4)2 + 80 can be obtained by the transformation of y = x2.
b) Interpret the equation of the transformed function to find the maximum height reached by the flare and the time it takes to reach this height.
3. Describe how the graph of y = 4cos(2(x - 3)) + 1 is related to the graph of y = cos x. (2 marks)
Lesson 5 Inverse of a Function
This is a Project Based course.
Here is the link for your project. Scroll down to the bottom of the module. Please check it out before you proceed - it is half of your module grade.
Lesson Questions
- determine the graph of the inverse of f(x) given the graph of f(x)
- determine the equation of the inverse of f(x) given the equation of f(x)
Lesson
Click on Lesson 5 and work through the whole lesson. You can expect this to take about three hours before doing the project work. Remember that the Assignment is for practice and NOT to be handed in.
Link to Learn Everywhere lessons
Multimedia
Self Check Quiz
Each lesson will have a quiz to help you know how you are doing. You have three chances for each quiz and we count the best score only.
Project work
Module 1 Transformations Wrap-up
Module 1 Wrap-up
You are nearing completion of the first Module in this course.
Here is the link to submit your project.
Here is a link to the Project rubric
The final part of this Module is the Test
Benchmark solutions
Stretches:1. a) a = 1/2, b = 3
b) a = 3, b = 1/2
c) a = 4, b = 2
d) a = 1/2, b = 1/4
Combinations:
1. a) reflection in the y axis, translation right 2 units
b) horizontal compression by a factor of 1/2, translation left 4 units and downward 4 units
c) reflection in the y axis, translation right 4 units and upward 5 units
d) horizontal compression by a factor of 1/3, translation right 2 units and upward 8 units
2. a) vertical expansion by a factor of 5, reflection in the x axis, translation right 4 units and upward 80 units.
b) The vertex (0,0) of y = x2 is moved to (4, - 80). the maximum height is 80 m, after 4 seconds.
3. The graph of y = 4cos(2(x - 3)) + 1 is the image of y = cos x after a vertical stretch by a factor of 4, a horizontal stretch by a factor of 1/2, and translation of 3 units right and 1 unit up.