I have solved the questions I just need to know if it is correct. Linear algebra

Math 107 Quiz 4

Professor: Dr. Kamal Hennayake

Name________________________________

Instructions:

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The quiz is worth 50 points. There are 10 problems, each worth 5 points. Your score on the quiz will be

converted to a percentage and posted in your assignment folder with comments.

This quiz is open book and open notes, and you may take as long as you like on it provided that you

submit the quiz no later than the due date posted in our course schedule of the syllabus. You may refer

to your textbook, notes, and online classroom materials, but you may not consult anyone.

You must show all of your work to receive full credit. If a problem does not seem to require work, write

a sentence or two to justify your answer.

Please type your work in your copy of the quiz, or if you prefer, create a document containing your

work. Scanned work is also acceptable. Be sure to include your name in the document. Review

instructions for submitting your quiz in the Quizzes Module.

If you have any questions, please contact me by e-mail (kamal.hennayake@faculty.umuc.edu).

At the end of your quiz you must include the following dated statement with your name typed in lieu of

a signature. Without this signed statement you will receive a zero.

I have completed this quiz myself, working independently and not consulting anyone except the instructor. I

have neither given nor received help on this quiz.

Name:

Date:

Please remember to show ALL of your work on every problem. Read the basic rules for

showing work below BEFORE you start working on the quiz.

a) Each step should show the complete expression or equation rather than a piece of it.

b) Each new step should follow logically from the previous step, following rules of algebra.

c) Each new step should be beneath the previous step.

d) The equal sign, =, should only connect equal numbers or expressions.

If you have questions about showing work, please ask.

Math 107

Quiz 4

Page 2

Did you read the rules for showing work on page 1 of the quiz? If not, please go back to page 1 now and

read them. If you do not show work correctly, you will not earn full credit.

1) Sketch the graph of the given function. (Make sure to show work to earn points)

(a)

𝑓𝑓(𝑥𝑥) = −𝑥𝑥 2 − 12𝑥𝑥 + 32

Give the vertex:

(b) Give the x-intercept(s) as a point:

(c)

Give the y-intercept as a point:

(d) Give the range as an interval:

(e)

Graph the function on the Cartesian plane on the left.

2) Solve the following inequality. Show work clearly to earn points. Give the answer using interval notation.

5𝑥𝑥 2 + 26𝑥𝑥 + 5 < 0
Math 107
Quiz 4
Page 3
3) Consider the polynomial function, 𝑓𝑓(𝑥𝑥) = 3𝑥𝑥(𝑥𝑥 − 4)2 (𝑥𝑥 + 2)3 . Find the following information. Show work
clearly for credit.
(a) Find the real zeros of the polynomial and their corresponding multiplicities. Indicate whether the graph
crosses the x-axis or touches and turns at the zero.
Zeros
Multiplicities Behavior at the zero
(b) End behavior:
(c) y-intercept:
(d) Provide a rough sketch of the graph:
4) Consider the polynomial function, 𝑓𝑓(𝑥𝑥) = −𝑥𝑥 4 + 5𝑥𝑥 2 − 4. Find the following information. Show work
clearly for credit.
(a) Find the real zeros of the polynomial and their corresponding multiplicities. Indicate whether the graph
crosses the x-axis or touches and turns at the zero.
Zeros
Multiplicities Behavior at the zero
(b)
(c)
(d)
(e)
(f)
(g)
Degree:
Leading term:
Leading coefficient:
Constant term:
End behavior:
Provide a rough sketch of the graph
Math 107
Quiz 4
Page 4
7𝑥𝑥−5
5) Consider the rational funciton, 𝑓𝑓(𝑥𝑥) =
to find the followings. Show work or give a justification.
7𝑥𝑥+4
(a) Domain in interval notation:
(b) Equations of vertical asymptotes:
(c) Equation of horizontal asymptote:
(d) x-intercepts at the points:
(e) y-intercept at a point:
2𝑥𝑥−8
6) Consider the rational funciton, 𝑓𝑓(𝑥𝑥) = 2 to find the followings. Show work or give a justification.
𝑥𝑥 −9
(a) Domain in interval notation:
(b) Equations of vertical asymptotes:
(c) Equation of horizontal asymptote:
(d) x-intercepts at the points:
(e) y-intercept at a point:
Math 107
Quiz 4
Page 5
𝑥𝑥 2 −4𝑥𝑥+3
7) Consider the rational funciton, 𝑓𝑓(𝑥𝑥) = 2
to find the followings. Show work or give a justification.
𝑥𝑥 −8𝑥𝑥+7
(a) Equations of vertical asymptotes:
(b) Equation of horizontal asymptote:
(c) Hole at a point:
(d) x-intercepts at the points:
(e) y-intercept at a point:
(f) Sketch a rough graph of the function. Be sure to draw any asymptotes as dashed lines.
8) Consider the rational funciton, 𝑓𝑓(𝑥𝑥) =
(a) Equations of vertical asymptotes:
𝑥𝑥 2 −5𝑥𝑥+6
5𝑥𝑥−7
to find the followings. Show work or give a justification.
(b) Equation of oblique asymptote:
(c) x-intercepts at the points:
(d) y-intercept at a point:
(e) Sketch a rough graph of the function. Be sure to draw any asymptotes as dashed lines.
Math 107
Quiz 4
Page 6
9) Solve the followings rational inequality. Show work to earn points. Express your answer using interval
notation.
𝑥𝑥 − 4