Umuc math 107 final exam answers

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. MAKE CERTAIN YOUR SUBMITTAL IS CLEARLY READABLE. FOR THE SHORT ANSWER SECTIONS make sure your ANSWER IS CIRCLED 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

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.

MAKE CERTAIN YOUR SUBMITTAL IS CLEARLY READABLE. FOR THE SHORT ANSWER SECTIONS make sure your ANSWER IS CIRCLED

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._______

A. Domain [ -5, 5]; Range [- 6, 6]

B. Domain [- 4, 5]; Range [- 6, 6]

C. Domain [- 6, 5]; Range [- 4, 6]

D. Domain [- 6, 6]; Range [- 4, 5]

2. Solve: x = √−8x + 9 and check your solution(s) 2.________

A. x = - 9

B. x = 1

C. x = {-9, 1}

D. No Solution

2 of 11

3. Determine the x interval(s) on which the function is increasing. 3.__________

A. (−4, 0] and [4, ∞)

B. [0, 4]

C. (−∞, 3) ∪ [−1, 5 ]

D. (−∞, −4] and [0, 4 ]

4. Determine whether the graph of Y = | x | - 3 is symmetric with respect 4. _________

to the origin, the x-axis, or the y-axis.

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. Find the solution to the inequality : | 6 – x | + 3 < 8 5. ___________

A. (𝟔, ∞)

B. (𝟏 , 𝟏𝟏 )

C. (−∞, 𝟏) ∪ (𝟏𝟏, ∞)

D. (−1, −𝟏𝟏)

3 of 11

6. Which of the following represents the graph of −3x + 5y = 15 ? __________

A. B.

C. D.

7. Write a slope-intercept equation for a line perpendicular to the line −3x + 5y = 15

which passes through the point (6, – 5).

A. y = − 𝟓

𝟑 𝒙 + 𝟓

B. y = 𝟓

𝟑 𝒙 − 𝟏𝟓

C. y = − 𝟑

𝟓 𝒙 + 𝟓

D. y = 𝟑

𝟓 𝒙 − 𝟏𝟓

4 of 11

8. Choose what type of graph is below ? 8.___________

A. It is not a function.

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

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

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

9. Express as a single logarithm: log (2x + 1) + log 2x - 4 log x 9.__________

A. log ( 4x+1

4x )

B. log ( 2x(2x+1)

4x )

C. log ( 4x2 - 2x)

D. log ( 2𝑥 (2𝑥 + 1)

𝑥4 )

10. Which of the functions correspond to the graph? 10.__________

A. f(x) = e x

B. f(x) = e x – 1

C. f(x) = log(x)

D. f(x) = log(x) – 1

5 of 11

11. Suppose that for a function f(x), that it has exactly 1 zero (or 1 X-intercept)

Which of the following statements MUST true? (only one answer is correct) 11. _________

A. f(x) is linear and has a positive slope.

B. f(x) is a quadratic

C. The equation for f(x) = 0 has a complex solution with one real part which = 0.

D. There is exactly one point on the graph of f(x) which has an x-coordinate = 0.

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 equations are given.) What is the relationship between g(x) and f (x)? A,B,C, or D 12. __________

A. g(x) = f(x – 4) + 2 B. g(x) = f(x + 2) – 4

C. g(x) = f(x + 4) + 2 D. g(x) = f(x – 2) – 4

The following problems are SHORT ANSWER:

13. Multiply and simplify: (5 + 2i)(6 − i).

Write the answer in the form a + bi, where a and b are real numbers. 13. ____________________________

14. Solve the inequality for x, write the answer in interval notation:

𝐱 − 𝟓

𝐱 ≤ 𝟎 14. __________________________

6 of 11

15. A cup of coffee is at 200˚ F. It is placed in a room of constant temperature of 70˚ F.

The temperature T of the coffee x (minutes) after it is placed in the room is given by the equation:

T(t) = 70 + 130 e – 0.051 x

Find the temperature of the soup 50 minutes after it is placed in the room. (Round to the nearest degree F )

15. ________________

16. Find the value of x : 𝐱 = 𝐥𝐨𝐠𝟓 ( 𝟏

𝟏𝟐𝟓 ) 16. ________________

17. Find the value of x : 3 x - 1 = 81 17. ________________

18. If one invested $10,000 in an account with an annual interest rate of 4.5% compounded monthly,

what will be the total amount after 25 years? (do not round values until final answer) then give answer to

nearest cent.

18. ________________

7 of 11

19. For the quadratic f(x) = x2 – 6x + 5

a) Give the vertex point as an ordered pair (x, y) ? ________________

b) Give the x intercept(s) as ordered pairs (x,y) ________________ , ______________

c) Give the interval notation of X where the function increasing? ________________

20. Consider the Polynomial in factored form: f(x) = ( 𝟏

𝟒 )(x - 3)(x + 2)(x - 1)

a) Which sketch illustrates the end behavior ? __________

A. B. C. D.

b. Give the y-intercept of f(x) as an ordered pair (x,y) __________

c. Give the zeroes of the function as ordered pairs (x,y) _________________

d. State which graph (A,B,C,or D) below is the graph of f(x) ____________

A B C D

8 of 11

21. Let f(x) = 𝐱 − 𝟏

𝟐𝐱 − 𝟓

(a) State the domain in interval notation: Answer: _________________

(b) State the vertical asymptote(s) as an equation. Answer: _________________

(c) State the horizontal asymptote as an equation. Answer: _________________

(d) Which of the following represents the graph of f(x) = 𝐱 − 𝟏

𝟐𝐱 − 𝟓 Answer: ________

A B

C D

9 of 11

SHORT ANSWER Must show work for credit where indicated!!

22. Let f(x) = √𝒙 + 𝟕 and g(x) = x + 3

a) Find ( 𝒇

𝒈 ) (𝟐) show work. ________________

b) Give the domain of the function ( 𝒇

𝒈 ) (𝐱) in interval notation __________________________

23. Given two points (6, - 2) and (- 4, 3) Must show work for credit

a) what is the distance between the 2 points? ________________

b) what is the midpoint between the 2 points? as an ordered (x,y) pair ________________

c) what is the slope (m) of the line that connects the two points? m = ________________

give as a fraction or whole number (not a decimal)

24. Find the equation of a line which passes through the points (-2, 3) and (1, 9) expressed in slope intercept form. Must show work for credit

10 of 11

25. Let f(x) = x2 + 5 and g(x) = x - 3 Must show work for credit.

a. Find the composite function (𝐟 ∘ 𝐠)(𝐱) and simplify.

b. Find the value of: (𝐟 ∘ 𝐠)(𝟏)

26. Given the function f(x) = 𝟑𝐱 − 𝟏

𝟒 find the inverse function f-1(x). Must show work for credit.

27. Solve for the zeros of the equation: 2x2 = − 8x + 10 Must show work for credit.

28. Someone throws a baseball upward where the height (in feet) as a function of time (sec) is given by

h(t) = −16t2 + 80t (feet) Must show work for credit.

a. Find the time t when the ball is at the maximum height? ______________________

(include units)

b. What is the maximum height of the ball at the time t you found in a. ___________________ (include units)

11 of 11

29. Solve for x value(s) : x

x−4 =

32

x2 − 4x Must show work for credit.

30. Find the complex solution to the function f(x) = 3x2 +2x + 4 Must show work for credit.

and simplify your answer.

Last Page! You did it!

Check your work!

a. Check that you copied the problem correctly

b. for simple sign errors

c. for simple arithmetic errors

d. show work where indicated

e. check your for extraneous solutions (that are not valid)

e. make sure your answer is clearly indicated.