Complete the following questions for tomorrow’s lesson.
Page 125 questions 28 and 29
Quadratics + Rational Functions Homework Assignment
Complete the questions in the file attached here and submit your work electronically (as a PDF).
Your file should be received before the beginning of our lesson on Sunday, November 13th. Note that the two bonus questions are optional, but I would encourage everyone to try at least one!
As always, you can write any questions you have about the assignment below in the comments section.
Quadratics + Even and Odd Functions
For tomorrow’s lesson complete the following questions.
Pages 110–112 questions 28, 30, 31, 43
Also, see if you can answer the following question: Is the sum of two odd functions always an even function? (And similarly, is the sum of two odd functions always an odd function?)
Quadratic Functions Homework
Complete the following question for our next lesson on Tuesday. Remember, you can leave a comment below if you run in to any trouble with these!
Consider the quadratic function \(f(x) = 2x^2 + 4x -16\).
- Express \(f\) in factored form.
- Express \(f\) in vertex form.
- Describe a sequence of transformations that would produce the graph of \(y = f(x)\), starting from the graph of \(y = x^2\).
- Describe a sequence of transformations different from your answer to c) that would also produce the graph of \(y = f(x)\), starting from the graph of \(y = x^2\).
Rational Functions and Horizontal Asymptotes
Try to answer these questions for our next lesson. Can you suggest an answer to question 3?
Consider the functions given below.
\[f(x)=x^3-2x\qquad g(x)=x^2+4x\qquad h(x)=2x^2+5x-1\]
- Form the six possible rational functions using \(f\),\( g\), and \(h\).
- Which of the rational functions you have produced have horizontal asymptotes? For any functions that have horizontal asymptotes, write down the equation of that asymptote.
- How can you tell when a rational function will have a horizontal asymptote? How can you determine the equation of that asymptote?
Rational Functions
Here’s the function that was introduced at the end of the last lesson.
\[f(x) = \frac{5x-6}{x+2}\]
Can you determine the \(x\)-axis intercepts and any asymptotes for the graph of \(y=f(x)\)?
We’ll discuss this question in today’s lesson.
Transformations of Functions Test [Updated]
On Tuesday, October 18th we’ll have a test on transformations of functions.
The following questions will be useful in preparing for the test.
Pages 84–85 questions 1, 2, 4, 19
Pages 86–89 questions 5, 6, 13, 14, 23
Update: Not that calculators will not be permitted for this test.
Composites and Inverse Functions Test
On Wednesday, September 28th we’ll have our first HL test on composite and inverse functions.
The following list of questions should be completed as part of your review of this material, and we can discuss any problem you may be having in class before the test.
Pages 85–89 questions 1 to 4, 9 to 11, 15 to 22
Composite and Inverse Functions
Complete the following questions for Sunday, the 18th of September.
Composite Functions
Pages 60–61 questions 1, 2, 5, 6, 9, 10, 12, 17, 19, 24, 25
Inverse Functions
Pages 68–69 questions 15, 16, 17, 24, 30, 31, 34, 35, 36, 37, 38
12 HL Composite Functions Homework
Let \(f(x)=x^2\) and \(g(x)=x-1\).
- Find the range of \(f\) and \(g\), assuming the domain for both is \(\mathbb{R}\).
- Find the range of \(f\) and \(g\), assuming the domain for both is \([-2,\infty[\).
- Find the value of each of the functions below when \(x=4\).
a) \(f\circ g\)
b) \(g\circ f\) - Find the range of each of the functions in Question 3.