MATh107 exam 3

Math 107 Section 6384 – Exam #3 – Due February 22, 2015 – page 1 of 4

Follow these directions carefully.

• This exam is due by 11:59 PM Eastern time on February 22, 2015.

o This is an important assignment, counting 12% of your course grade.

o Submit this assignment in your assignments folder by the due date.

• Answer all the questions.There are 23 problems on 3 pages.

o There are 115 points possible. I will grade all the problems and convert your total score to a

percentage out of 100.

o No work is requiredfor the MULTIPLE CHOICE SECTIONor for the SHORT ANSWER SECTION. There isno partial credit for these problems, soplease work carefully.

o Show all workfor the LONG ANSWER SECTION.There is partial credit for these problems.

• Answer these questions on separate pages (not these sheets).

o Use a separate document to solve these problems. You may type your answers in a document (like Word or Excel) or handwrite your answers and scan them in – up to you.

o Submit your assignment asan attachment.

Use filename 1501Math107_6384_E3_LastName_FirstName.*

• You must work on your own, consulting no other person except for me. You can of course use yourbook, calculator, and any other resources, besides people, that you may have at your disposal.

MULTIPLE CHOICE SECTION. Choose the best alternative. (2 pts each)

1. Solve: 2m²?m+9=0.

a)		1±		73				c)			1	±			71		i
4						4		4
		1									1±
b)		±			35		i	d)		71
4					4
			4

2. Solve: 5x?6=20.

a)	?	14	,	26		c)	?70,130
	5	5
b)	?	26	,	26		d)		26
			5
	5	5

3. Solve: 4?3x?2.

a)	[2, 2 / 3]	c)	[2 / 3, 2]
b)	(??, 2 / 3] ?[2,?)	d)	(??, 2]?[2 / 3,?)

4. Solve: 2?5x?3.

a)	[?1 / 5,1]	c)	(??,?1]?[1 / 5,?)
b)	(??,?1 / 5]?[1,?)	d)	[1,?1 / 5]

5. Solve: x²?3x?10>0.

a)	(??,?5)? (2,?)	c)	(?2, 5)
b)	(?5, 2)	d)	(??,?2)? (5,?)

Math 107 Section 6384 – Exam #3 – Due February 22, 2015 – page 2 of 4

6.	Solve:		x?5	? 0.
			x+ 2		(?2, 5]
	a)	(??,?5]? (2,?)	c)
	b)	(?2, 5)	d)	(??,?5)? (?2,?)
7.	For the graph of the function	f(x)=2x2?12x+14,find the vertex.
	a)	(3,4)		c)	(?4, 3)
	b)	(6,14)	d)	(3,?4)

8. The Shanghai World Financial Center is about 1614 feet tall. How long would it take an object falling

freely from the top to reach the ground?

a)	About 10.0 sec	c)
b)	About 50.4 sec	d)

Uses =16t ² . About 2.5 sec About 100.9 sec

9.	Solve			= x?3.
	? 3x
	a)	No solution	c)	5
	b)	11/2		d)	?2, 5

10. State the tail behavior off(x)=?5x³?6x²+2x?1. Refer to the instructions for Exercises 11-18 on page 306 in Section 4.1 of the textbook, and classify the tail behavior as one of the pictures labeled a), b), c), or d).

11. State the tail behavior off(x)=6x⁸?3x²+4. Refer to the instructions for Exercises 11-18 on page 306 in Section 4.1 of the textbook, and classify the tail behavior as one of the pictures labeled a), b), c), or d).

12.	Find the vertical asymptote of	f(x)=	x?6	.
(x? 2)2
		x=?3
	a)	c)	x=	2
	b)	x=6	d)	x=	?2

13. Determine the domain of f(x)=x²+ x?12.

a)	(??, 4)? (3,?)	c)	(??,?4]?[3,?)
b)	(??,?3]?[4,?)	d)	[?4, 3]

Math 107 Section 6384 – Exam #3 – Due February 22, 2015 – page 3 of 4

SHORT ANSWER SECTION.Be careful; there is no partial credit for these questions.

Questions 14 and 15refer to the polynomial f(x)=3x(x?3)²(x+2)³(x²?3).

14. This function has five zeros. Complete the table. List each of the zeros (there are five), and the

multiplicity of each. (Each lettered problem is worth 2 pts each)

Zero

Multiplicity

a)

b)

c)

d)

e)

15.

Determine the degree of this polynomial.

(2 pts)

In Questions 16, 17, and 18,write in simplesta+biform.

(3 pts each)

16.

49

25

? 100

17.

(1? 4i)(7 + 6i)

18.	2? i
3	? 2i

LONG ANSWER SECTION.Solve the problems. You must show all work in order to receive any credit.

19. Consider the quadratic function f(x)=?x²+2x+8

	a.	Find the vertex.	(4 pts)
	b.	State whether there is a maximum or minimum value and find that value.	(4 pts)
	c.	Find the domain.	(1 pt)
	d.	Find the range.	(2 pts)
	e.	Find the interval(s) on which the function is increasing.	(2 pts)
	f.	Find the interval(s) on which the function is decreasing.	(2 pts)
	g.	Find the coordinates of the x-intercepts of the graph of this function.	(4 pts)
	h.	Find the coordinates of the y-intercept of the graph of this function.	(3 pts)
	i.	Sketch the graph of the function.	(4 pts)
			5x
20.	Suppose that f(x)=		.
x2? x?6
	a.	Determine the domain of f.	(5 pts)
	b.	Determine the vertical asymptote(s), if any, of the graph of f .	(6 pts)
	c.	Determine the horizontal asymptote(s), if any, of the graph of f .	(3 pts)
	d,	Sketch the graph of f.	(6 pts)

21. A homeowner wants to fence a rectangular garden using 60 ft of fencing. An existing stone wall will be used as one side of the rectangle. Find the dimensions for which the area is a maximum. (10 pts)

Math 107 Section 6384 – Exam #3 – Due February 22, 2015 – page 4 of 4

22. Classic Furniture Concepts has determined that when x hundred wooden chairs are built, the average cost

per chair is given byC(x)=0.1x2?0.7x+1.625, whereC(x) is in hundreds of dollars.
a.	How many chairs should be built to minimize the average cost per chair?	(6 pts)

b. For the number of chairs you found in part a), what is the average cost? That is, what is the least

average cost per chair? (6 pts)

In this problem, be careful. The variable x is in hundreds, and the variable y is in hundreds of dollars.

So, if you find x = 2, that is 200 chairs. You need to find C(2) = 0.625, which is 0.625 hundred dollars, or $62.50. (Of course, these are not the correct values.)