Home Β» MATH 107 UMBC Rational Function and Complex Numbers Questionnaire

MATH 107 UMBC Rational Function and Complex Numbers Questionnaire

MATH 107 Quiz 4MATH 107_SU21 QUIZ 4
Name:_ Jonathan Russe____
Date:_7/24/2021_
Please show your work for all problems, and express your answers using exact values. Express fractions
in simplest form, including rationalizing all denominators. Write complex numbers in the form π‘Ž + 𝑏𝑖.
Problem/Solution
1
score
Find all real and non-real solutions.
a) (π‘₯ 2 βˆ’ 1)(3π‘₯ βˆ’ 2) = π‘₯(π‘₯ + 1)(π‘₯ βˆ’ 2) βˆ’ 3(π‘₯ βˆ’ 1)
b) 2𝑦 2 βˆ’ 2√3𝑦 βˆ’ 3 = 𝑦 2 βˆ’ 5
2
Find all solutions. Write any complex numbers in the form π‘Ž + 𝑏𝑖.
2π‘₯ + 1 =
3
3π‘₯ 2 + 4π‘₯ + 3
π‘₯+2
For the polynomial function 𝑓(π‘₯) = (π‘₯ βˆ’ 1)2 (2π‘₯ + 3)
a) State the leading term, leading coefficient, a, and degree, n.
b) Describe the end behavior.
c) Find the zeros and the multiplicity, m, of each. State whether the graph will
cross the x-axis or rebound at each of the zeros.
d) For each interval, evaluate the function using a test point. Use your results
to create a sign chart.
4
The height a model rocket reaches can be described by the function β„Ž(𝑑) = βˆ’16𝑑 2 +
180𝑑 where t = time in seconds h = height in feet.
Page 1 of 3
MATH 107 Quiz 4
a) How long does it take the rocket to reach maximum height? Round time to
two decimal places.
b) What is its maximum height? Round down to the nearest foot.
5
Continuation of question 4
a) From a nearby viewpoint, onlookers can see the rocket when it is at least
360 ft above the ground. During what times after liftoff is the rocket visible
from this viewpoint (round to two decimal places)?
b) Based on your result from part c), do you expect the rocket to be visible from
the viewpoint 10 seconds after liftoff? Confirm your answer by calculating
the rocket’s height for this time.
6
For the rational function 𝑓(π‘₯) =
2π‘₯ 2 βˆ’3π‘₯βˆ’9
π‘₯ 2 βˆ’3π‘₯
a) State the domain using interval notation.
b) Write the equation of any vertical asymptotes.
c) Identify the coordinates of any holes.
7
Continuation of question 6
a) Write the equation of any horizontal asymptotes. Explain your reasoning.
b) Using Desmos, create the graph, showing any holes and showing
asymptotes as dashed lines. Include axis labels.
8
Continuation of question 6 – 7
Page 2 of 3
MATH 107 Quiz 4
a) State the behavior of the function as it approaches any vertical asymptotes.
b) State the behavior of the function as it approaches any horizontal
asymptotes.
9
Given the function𝑓(π‘₯) =
inequality
π‘₯ 2 βˆ’5π‘₯+4
, use
π‘₯+4
the following steps to solve the rational
π‘₯ 2 βˆ’ 5π‘₯ + 4
β‰₯0
π‘₯+4
a) Identify the zeros of the function.
b) Identify any asymptotes and/or holes.
c) For each interval, evaluate the function using a test point. Use your results
to create a sign chart.
d) State the solution set of the rational inequality using interval notation.
10 Solve the equation and show the check of your work.
π‘₯
π‘₯ βˆ’ 1 π‘₯ 2 + 3π‘₯ βˆ’ 1
βˆ’
=
π‘₯ + 1 π‘₯ + 2 π‘₯ 2 + 3π‘₯ + 2
Page 3 of 3

Place your order
(550 words)

Approximate price: $22

Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
$26
The price is based on these factors:
Academic level
Number of pages
Urgency
Basic features
  • Free title page and bibliography
  • Unlimited revisions
  • Plagiarism-free guarantee
  • Money-back guarantee
  • 24/7 support
On-demand options
  • Writer’s samples
  • Part-by-part delivery
  • Overnight delivery
  • Copies of used sources
  • Expert Proofreading
Paper format
  • 275 words per page
  • 12 pt Arial/Times New Roman
  • Double line spacing
  • Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read more

Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read more

Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read more

Privacy policy

Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read more

Fair-cooperation guarantee

By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more

Order your essay today and save 30% with the discount code ESSAYHELP