Category: 11 HL Homework

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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.

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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?)

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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 \(f(x) = 2x^2 + 4x -16\).

  1. Express \(f\) in factored form.
  2. Express \(f\) in vertex form.
  3. Describe a sequence of transformations that would produce the graph of \(y = f(x)\), starting from the graph of \(y = x^2\).
  4. 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 \(y = x^2\).
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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.
\[f(x)=x^3-2x\qquad g(x)=x^2+4x\qquad h(x)=2x^2+5x-1\]

  1. Form the six possible rational functions using \(f\),\( g\), and \(h\).
  2. 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.
  3. How can you tell when a rational function will have a horizontal asymptote? How can you determine the equation of that asymptote?
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Review: The Derivative Part 3 + Assignment

Attached below are the final review notes for the summer.

Derivatives Review Notes (Complete)

Again, this document contains all prior review notes, so you won’t need to refer to the earlier versions when working through this material.

The newly added sections focus on using the graph of the derivative (and the second derivative) to discover features of the graph of the original function, as in applications of Calculus it’s often the case that we understand more about the derivative than we do about the original function.

Also included below is your assignment,  due on the 29th of August (your second day back). I’ve marked the last two questions (4 and 5) with a star, as they are optional (though I would strongly encourage you to do those as well). As always, post any questions below!

12 HL Derivatives and Curve Sketching Assignment

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Derivatives and Curves [Updated]

Complete the following question for tomorrow’s lesson.

Use the derivative of the function \[f(x)=x^3-x^2+2x-1\] to find the coordinates of the (local) extrema of \(f\).

Update: Oops! The function above has no extrema! (How can you tell from the first derivative?) However, it does have what’s called a point of inflexion, which is a point at which the function changes concavity (from concave up to concave down, or vice versa). Can you find the coordinates of the point of inflexion?

At any rate, the function \(g\) below does have extrema, so you should find the coordinates of the extrema of \(g\). Can you also find the coordinates of its point of inflexion?

\[g(x)=x^3-x^2-2x-1\]