Professor Poirier | D328 | Fall 2024

Test #2 review part 1

Comment due Sunday, October 27

Test #2 will be given in class Monday, October 28. The format will be similar to the format of Test #1.

Recall from Test #1 one question asked you a series of conceptual true/false questions where you had to justify your answer. Another question asked you for a series of examples of mathematical objects (mostly functions) satisfying certain conditions.

To prepare for Test #2, for part 1 of this week’s OpenLab assignment, you will comment on this post with two questions that you come up with yourself, as well as their answers.

  1. Your first question should be conceptual and phrased as a statement which is either always true or always false. Your answer should indicate whether the statement is true or false together with a sentence explaining the answer.
  2. Your second question should be asking for an example of a mathematical object satisfying certain conditions. Your answer should provide this example together with together with a sentence explaining the example and why it satisfies the conditions.

You can use the Test #1 questions for inspiration (the different versions of the tests had similar questions, so check out your classmates’ solutions—when they appear—for the other versions).

Try to focus on the material covered in class since Test #1. You can see the list of topics on the schedule.

7 Comments

  1. Justin

    1. when trying to find the root of a polynomial do we use quadratic equation true or false?

    2. A math equation that has to obey certain conditions would be the inverse function. The conditions it has to follow if trying to find the inverse of the equations by using f(-1)x.

  2. Naz

    When dividing a polynomial f(x) by g(x) = x−c, the actual calculation of the long division has a lot of unnecessary repetitions, and we may want to reduce this redundancy as much as possible. In fact, we can extract the essential part of the long division, the result of which is called synthetic division.

  3. summerna

    1. True or False- Every polynomial function is also a rational function.
    2. Give an example: equation of a graph with no horizontal asymptote

    Answers:

    1. True– a rational function is a function f(x) that can be written as f(x) = p(x) / q(x) aka polynomial/polynomial
    2. f(x) = x/1 ; Since x, the numerator, is in degree 1, its degree is greater than in the denominator, 1, which has degree 0, therefore the graph has no horizontal asymptote
  4. Cindip

    1. Give an example of an equation that has the vertical asymptote of -1 and 3.

    Answer: (x+2)/ (x+1)(x-3). This is an example of a vertical asymptote because it remains in the denominator even after cancellation.

    2.The domain of every polynomial function f(x) is (-∞,∞) with no restrictions. 

    Answer: The answer is TRUE because all polynomials can have any number input that will have some output. Unless it’s in the denominator, it doesn’t require a restriction. 

  5. Omaima

    1. Every polynomial has horizontal asymptote’s. True or false?

    Is false because polynomial does not need to have a horizontal asymptote.

  6. Mitchel Enoe

    1)

    Question: For any two polynomials P(x) and Q(x), the degree of the product P(x)times Q(x) is always equal to the sum of the degrees of P(x) and Q(x).

    Answer:This statement is false because even though it may be true most of the time, its not always. for example, if either P(x) or Q(x) is the zero polynomial (which has no degree or can be thought of as having degree −infinity then the degree of the product will not be the sum of their degrees but rather undefined or simply zero. For example, if P(x)=0, the degree of P(x)⋅Q(x) is 0, regardless of the degree of Q(x)

    2)

    Question:Give a polynomial of degree 3 with integer coefficients that has exactly one real root and two complex conjugate roots.

    Answer:

    The polynomial f(x)=x^3−3x+2f(x) satisfies the given conditions. Because the polynomial x^3 – 3x + 2 has the following roots: x=1,x=−1±i. It has one real root, x=1, and two complex conjugate roots, x=−1+i and x=−1−i. This satisfies the condition of having one real root and two complex conjugate roots, as required for a cubic polynomial with integer coefficients.

  7. j.a

    Javon

    Question 1:

    The graph of a rational function may have more than one horizontal asymptote

    True or False

     

    This statement is  false because at most a rational function can only have one horizontal asymptote due to how the end behavior of the function is determined by the highest degree terms.

    Question 2:

    Give an example of a function that has a hole at x=5

    (x + 4) (x – 5)

    _______________________

       (x+6)      (x-7)      (x -5)

    In order for there to be a hole there has to be two similar binomials

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