(Answered)-I would need the answers to 15,18,20,22,23,24,25,26,29. The

I would need the answers to 15,18,20,22,23,24,25,26,29. The equations that need work shown please show work.

College Algebra MATH 107

 

 

Spring, 2016, V4.9

 

 

MATH 107 FINAL EXAMINATION

 

This is an open-book exam. You may refer to your text and other course materials as you work

 

on the exam, and you may use a calculator. You must complete the exam individually.

 

Neither collaboration nor consultation with others is allowed.

 

Record your answers and work on the separate answer sheet provided.

 

There are 30 problems.

 

Problems #1?12 are Multiple Choice.

 

Problems #13?21 are Short Answer. (Work not required to be shown)

 

Problems #22?30 are Short Answer with work required to be shown.

 

MULTIPLE CHOICE

 

1. Determine the domain and range of the piecewise function.

 

 

1. ______

 

 

4

 

2

 

-4

 

 

2

 

 

-2

 

 

4

 

 

-2

 

-4

 

A.

 

B.

 

C.

 

D.

 

 

Domain (? ?, ?2] ? [? 0.5, 2]; Range [0, 3]

 

Domain [? 4, 2]; Range [? 1, 3]

 

Domain [? 2, ?0.5]; Range [?1, 0]

 

Domain [? 1, 3]; Range [? 4, 2]

 

 

2. Solve:

 

A.

 

B.

 

C.

 

D.

 

 

15 ? 2 x = 6 ? x

 

 

2. ______

 

 

No solution

 

9

 

3

 

3, 7

 

 

Page 1 of 11

 

 

College Algebra MATH 107

 

 

Spring, 2016, V4.9

 

 

3. Determine the interval(s) on which the function is decreasing.

 

 

A.

 

 

(? 2, 2)

 

 

B.

 

 

(? 3.5, 3.5)

 

 

C.

 

 

(??, ?3.5) ? (0, 3.5)

 

 

D.

 

 

(? 5.3, 5.3)

 

 

3. ______

 

 

4. Determine whether the graph of y = x ? 5 is symmetric with respect to the origin,

 

the x-axis, or the y-axis.

 

4. ______

 

A.

 

symmetric with respect to the x-axis only

 

B.

 

symmetric with respect to the y-axis only

 

C. symmetric with respect to the origin only

 

D. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and

 

not symmetric with respect to the origin

 

 

5. Solve, and express the answer in interval notation:

 

A.

 

B.

 

C.

 

D.

 

 

7 ? 3x ? 17 .

 

 

5. ______

 

 

[?8, 10/3]

 

(??, ?10/3]

 

(??, ?10/3] ? [8, ?)

 

[?10/3, 8]

 

 

Page 2 of 11

 

 

College Algebra MATH 107

 

 

6. Which of the following represents the graph of

 

 

Spring, 2016, V4.9

 

 

4x ? 9y = 36 ?

 

 

A.

 

 

B.

 

 

C.

 

 

D.

 

 

6. ______

 

 

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College Algebra MATH 107

 

 

Spring, 2016, V4.9

 

 

7. Write a slope-intercept equation for a line parallel to the line x + 5y = 7 which passes through

 

the point (?10, 3).

 

7. ______

 

A.

 

 

1

 

y = ? x +1

 

5

 

 

B.

 

 

1

 

y = ? x+3

 

5

 

 

C.

 

 

y = ?5 x + 53

 

 

D.

 

 

y=

 

 

1

 

x+5

 

5

 

 

8. Does the graph below represent a function and is it one-to-one?

 

 

A.

 

B.

 

C.

 

D.

 

 

8. ______

 

 

It is a function and it is one-to-one.

 

It is not a function but it is one-to-one.

 

It is a function but not one-to-one.

 

It is not a function and it is not one-to-one.

 

 

Page 4 of 11

 

 

College Algebra MATH 107

 

 

9. Express as a single logarithm: 6 log x ? log y + log 1

 

A.

 

 

log ( 6 x ? y + 1)

 

 

B.

 

 

log ( 6x ? y )

 

 

C.

 

 

x +1

 

log

 

 

y

 

 

D.

 

 

x6

 

log

 

y

 

 

Spring, 2016, V4.9

 

 

9. ______

 

 

6

 

 

10. Which of the functions corresponds to the graph?

 

 

10. ______

 

 

A. f ( x ) = ?e x

 

B. f ( x ) = ?e x + 1

 

C. f ( x ) = e x ? 1

 

D. f ( x ) = e? x + 1

 

 

Page 5 of 11

 

 

College Algebra MATH 107

 

 

Spring, 2016, V4.9

 

 

11. Suppose that for a function f , the equation f (x) = 0 has exactly one real-number solution.

 

Which of the following statements MUST be true?

 

11. ______

 

A.

 

B.

 

C.

 

D.

 

 

f

 

f

 

f

 

f

 

 

has exactly one x-intercept.

 

has exactly one y-intercept.

 

is an invertible function.

 

is a linear function.

 

 

12. The graph of y = f (x) is shown at the left and the graph of y = g(x) is shown at the right. (No

 

formulas are given.) What is the relationship between g(x) and f (x)?

 

12. ______

 

 

-4

 

 

4

 

 

4

 

 

2

 

 

2

 

2

 

 

-2

 

 

4

 

 

-4

 

 

2

 

 

-2

 

 

-2

 

 

-2

 

 

-4

 

 

-4

 

 

y = f (x)

 

 

4

 

 

y = g(x)

 

A.

 

B.

 

C.

 

D.

 

 

g(x) = f (x ? 5) ? 2

 

g(x) = f (x + 2) ? 6

 

g(x) = f (x + 2) + 6

 

g(x) = f (x ? 2) ? 5

 

 

Page 6 of 11

 

 

College Algebra MATH 107

 

 

Spring, 2016, V4.9

 

 

SHORT ANSWER:

 

13. Multiply and simplify: (3 + 4i)(5 ? 8i).

 

Write the answer in the form a + bi, where a and b are real numbers.

 

 

Answer: ________

 

 

14. Solve, and write the answer in interval notation:

 

 

x+6

 

? 0.

 

x+2

 

 

Answer: ________

 

 

15. A bowl of soup at 190? F. is placed in a room of constant temperature of 80? F. The

 

temperature T of the soup t minutes after it is placed in the room is given by

 

 

T(t) = 80 + 110 e

 

 

? 0.075 t

 

 

Find the temperature of the soup 16 minutes after it is placed in the room. (Round to the nearest

 

degree.)

 

 

Answer: ________

 

 

1

 

16. Find the value of the logarithm: log 3 .

 

27

 

 

17. Solve:

 

 

76 x+1 = 49 .

 

 

Answer: ________

 

 

Answer: ________

 

 

18. Suppose $8,200 is invested in an account at an annual interest rate of 4.6% compounded

 

continuously. How long (to the nearest tenth of a year) will it take the investment to double in

 

size?

 

Answer: ________

 

 

2

 

 

19. Let f (x) = x + 4x + 12.

 

(a) Find the vertex.

 

 

Answer: ________

 

 

(b) State the range of the function.

 

 

Answer: ________

 

 

(c) On what interval is the function increasing?

 

 

Answer: ________

 

 

Page 7 of 11

 

 

College Algebra MATH 107

 

 

Spring, 2016, V4.9

 

 

20. Consider the polynomial P(x), shown in both standard form and factored form.

 

1

 

1

 

7

 

41

 

1

 

P ( x) = ? x 4 + x 3 + x 2 ? x + 3 = ? ( x + 3)( x ? 1)( x ? 2)( x ? 5)

 

10

 

2

 

10

 

10

 

10

 

(a) Which sketch illustrates the end behavior of the polynomial function?

 

 

A.

 

 

B.

 

vvvv

 

 

C.

 

vvvv

 

 

D.

 

vvvv

 

vvvv

 

 

Answer: ________

 

 

(b) State the y-intercept.

 

 

Answer: ________________

 

 

(c) State the zeros of the function.

 

 

Answer: ________________

 

Answer: ________

 

 

(d) State which graph below is the graph of P(x).

 

 

GRAPH A

 

 

GRAPH B

 

 

GRAPH C

 

 

GRAPH D

 

 

Page 8 of 11

 

 

College Algebra MATH 107

 

 

21. Let f ( x) =

 

 

Spring, 2016, V4.9

 

 

2+ x

 

.

 

3? x

 

 

(a) State the domain.

 

 

Answer: _________________

 

 

(b) State the horizontal asymptote.

 

 

Answer: _________________

 

 

(c) State the vertical asymptote(s).

 

 

Answer: _________________

 

 

(d) Which of the following represents the graph of f ( x ) =

 

 

2+ x

 

?

 

3? x

 

 

GRAPH A.

 

 

GRAPH B.

 

 

GRAPH C.

 

 

GRAPH D.

 

 

Answer: ______________

 

 

Page 9 of 11

 

 

College Algebra MATH 107

 

 

Spring, 2016, V4.9

 

 

SHORT ANSWER, with work required to be shown, as indicated.

 

22. Let f ( x) =

 

 

x ? 6 and g(x) = x ? 12 .

 

 

f

 

(a) Find (7) . Show work.

 

g

 

(b) Find the domain of the quotient function

 

 

f

 

. Explain.

 

g

 

 

23. Points (6, ?7) and (4, 1) are endpoints of the diameter of a circle.

 

(a) What is the length of the diameter? Give the exact answer, simplified as much as possible.

 

Show work.

 

(b) What is the center point C of the circle?

 

(c) Given the point C you found in part (b), state the point symmetric to C about the x-axis.

 

 

24. Find the equation for a line which passes through the points (9, ?1) and (6, 5). Write the

 

equation in slope-intercept form. Show work.

 

 

25. Kathy, a resident of Metropolis, pays Metropolis an annual tax of $60 plus 2.2% of her

 

annual income. If Kathy paid $1,105 in tax, what was Kathy?s income? Show work.

 

 

26. Let f (x) = 6x2 + 9 and g(x) = x + 5.

 

(a) Find the composite function ( f o g )( x ) and simplify. Show work.

 

(b) Find ( f o g ) (?3) . Show work.

 

 

27. Find the exact solutions and simplify as much as possible: 18x2 + 1 = 12x. Show work.

 

 

28. Given the function f ( x) =

 

 

1

 

x + 4 , find a formula for the inverse function. Show work.

 

7

 

 

Page 10 of 11

 

 

College Algebra MATH 107

 

 

Spring, 2016, V4.9

 

 

29. Donut Delights, Inc. has determined that when x donuts are made daily, the profit P (in

 

dollars) is given by

 

 

P(x) = ?0.002 x2 + 4.1x ? 1300

 

(a) What is the company?s profit if 600 donuts are made daily?

 

 

(b) How many donuts should be made daily in order to maximize the company?s profit? Show

 

work.

 

 

30. Solve:

 

 

x+5

 

28

 

= 2

 

. Show work.

 

x + 7 x ? 49

 

 

Page 11 of 11

 

 



 

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