Expert answer:30 Algerba questions with showing work. Questions

Expert answer: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 CHOICE1. Determine the domain and range of the piecewise function. 1. ______A. Domain [– 2, 4]; Range [– 2, 1]B. Domain [– 2, 4]; Range [– 4 , 2]C. Domain [– 4, 2]; Range [– 2, 4]D. Domain [0, 2]; Range [– 2, 0]2. Solve: 15 + 2x = − x 2. ______A. –3B. –3, 5C. –1/5D. No solution-4 -2 2 4-2-424College Algebra MATH 107 Fall, 2017, V3.2Page 2 of 113. Determine the interval(s) on which the function is decreasing. 3. ______A. (−¥,−1) and (1,3)B. (−5/ 3, 0) and (2,11/ 3)C. (−1,1) and (3,¥)D. (− 4 / 3, 1)4. Determine whether the graph of 3 y = x is symmetric with respect to the origin,the x-axis, or the y-axis. 4. ______A. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, andnot symmetric with respect to the originB. symmetric with respect to the x-axis onlyC. symmetric with respect to the y-axis onlyD. symmetric with respect to the origin only5. Solve, and express the answer in interval notation: | 7 – 5x | £ 8. 5. ______A. (–¥, –1/5]B. (–¥, –1/5] È [3, ¥)C. [– 1/5, 3]D. [– 1/5, ¥)College Algebra MATH 107 Fall, 2017, V3.2Page 3 of 116. Which of the following represents the graph of 9x − 4y = 36 ? 6. ______A. B.C. D.College Algebra MATH 107 Fall, 2017, V3.2Page 4 of 117. Write a slope-intercept equation for a line parallel to the line x – 7y = 3 which passes throughthe point (28, –5). 7. ______A.197y = x −B.157y = x −C. y = −7x +191D.117y = − x −8. Which of the following best describes the graph? 8. ______A. It is the graph of a function and it is one-to-one.B. It is the graph of a function but not one-to-one.C. It is the graph of an absolute value relation.D. It is not the graph of a function.College Algebra MATH 107 Fall, 2017, V3.2Page 5 of 119. Express as an equivalent expression: 2 log (x + 3) – 4 log y + log 1 9. ______A. log (2x + 7 − 4y)B.6log( )log(4 )xyC.249logxy + D.( )243logxy + 10. Which of the functions corresponds to the graph? 10. ______A. ( ) 2 1 x f x e− = −B. ( ) 1 x f x e− = +C. ( ) 2 x f x = −e +D. ( ) 2 x f x e− = +College Algebra MATH 107 Fall, 2017, V3.2Page 6 of 1111. Suppose that for a function f , the equation f (x) = 0 has no real-number solutions.Which of the following statements MUST be true? 11. ______A. f (x) > 0 for all x in the domain of f.B. f is an invertible function.C. f has no x-intercepts.D. f has no y-intercepts.12. The graph of y = f (x) is shown at the left and the graph of y = g(x) is shown at the right. (Noformulas are given.) What is the relationship between g(x) and f (x)?12. ______y = f (x) y = g(x)A. g(x) = f (x – 3) – 2B. g(x) = f (x – 2) – 3C. g(x) = f (x + 3) – 2D. g(x) = f (x + 2) – 32 -4 -2 4-2-424-4 -2 2 4-2-424College Algebra MATH 107 Fall, 2017, V3.2Page 7 of 11SHORT ANSWER:13. Multiply and simplify: (8 + i)(5 + 3i).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:205xx+£−. Answer: ________15. A can of soda at 78° F. is placed in a refrigerator that maintains a constant temperature of 35°F. The temperature T of the soda t minutes after it is placed in the refrigerator is given byT(t) = 35 + 43e– 0.058 tFind the temperature of the soda 12 minutes after it is placed in the refrigerator. (Round to thenearest tenth of a degree.)Answer: ________16. Find the value of the logarithm: 51log125 . Answer: ________17. Solve: 38x−5 = 9. Answer: ________18. Suppose $3,400 is invested in an account at an annual interest rate of 6.1% compoundedcontinuously. How long (to the nearest tenth of a year) will it take the investment to double insize? Answer: ________19. Let f (x) = x2 + 8x + 19.(a) Find the vertex. Answer: ________(b) State the range of the function. Answer: ________(c) On what interval is the function increasing? Answer: ________College Algebra MATH 107 Fall, 2017, V3.2Page 8 of 1120. Consider the polynomial P(x), shown in both standard form and factored form.P(x) = x3 − 3×2 − x + 3 = (x +1)(x −1)(x − 3)(a) Which sketch illustrates the end behavior of the polynomial function?Answer: ________(b) State the y-intercept. Answer: ________________(c) State the zeros of the function. Answer: ________________(d) State which graph below is the graph of P(x). Answer: ________GRAPH A GRAPH BGRAPH C GRAPH DA.B. C. D.vvvvvvvvvvvv vvvvCollege Algebra MATH 107 Fall, 2017, V3.2Page 9 of 1121. Let2( )3xf xx+=−.(a) State the domain. Answer: _________________(b) State the vertical asymptote(s). Answer: _________________(c) State the horizontal asymptote. Answer: _________________(d) Which of the following represents the graph of2( )3xf xx+=−? Answer: ______________GRAPH A. GRAPH B.GRAPH C. GRAPH D.College Algebra MATH 107 Fall, 2017, V3.2Page 10 of 11SHORT ANSWER, with work required to be shown, as indicated.22. Let f (x) = x – 3 and g(x) = x + 5 .(a) Find ) 1 (− gf. Show work.(b) Find the domain of the quotient functiongf. Explain.23. Points (1, –5) and (9, –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 (4, 3) and (6, –7). Write theequation in slope-intercept form. Show work.25. A salesperson earns a base salary of $2,100 per month and a commission of 6.5% on theamount of sales made. If the salesperson has a paycheck of $5,168 for one month, what was theamount of sales for the month? Show work.26. Let f (x) = 3×2 + 8 and g(x) = x – 4.(a) Find the composite function ( f o g)(x) and simplify. Show work.(b) Find ( f o g ) (−1) . Show work.27. Find the exact solutions and simplify as much as possible: 8×2= 3 + 8x. Show work.28. Given the function1( ) 59f x = − x , find a formula for the inverse function. Show work.College Algebra MATH 107 Fall, 2017, V3.2Page 11 of 1129. The Adventure Travel bus company has determined that when x tourists are given aparticular bus tour, the profit P (in dollars) is given byP(x) = –0.25 x2 + 25.50x – 220(a) What is the company’s profit if 32 tourists are given the tour?(b) How many tourists should be given the tour in order to maximize the company’s profit?Show work.30. Solve: 25 1202 4xx x++ =+ −. Show work.
math107_final_nov_2017_1.pdf

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College Algebra MATH 107
Fall, 2017, V3.2
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, 4]; Range [– 2, 1]
Domain [– 2, 4]; Range [– 4 , 2]
Domain [– 4, 2]; Range [– 2, 4]
Domain [0, 2]; Range [– 2, 0]
2. Solve: 15 + 2x = − x
A.
B.
C.
D.
2. ______
–3
–3, 5
–1/5
No solution
Page 1 of 11
College Algebra MATH 107
Fall, 2017, V3.2
3. Determine the interval(s) on which the function is decreasing.
A.
( −∞, −1) and (1,3)
B.
( −5 / 3, 0 )
C.
( −1,1) and ( 3, ∞ )
D.
( − 4 / 3, 1)
3. ______
and ( 2, 11/ 3)
4. Determine whether the graph of y = 3 x is symmetric with respect to the origin,
the x-axis, or the y-axis.
4. ______
A. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and
not symmetric with respect to the origin
B.
symmetric with respect to the x-axis only
C.
symmetric with respect to the y-axis only
D.
symmetric with respect to the origin only
5. Solve, and express the answer in interval notation: | 7 – 5x | ≤ 8.
A.
B.
C.
D.
5. ______
(–∞, –1/5]
(–∞, –1/5] ∪ [3, ∞)
[– 1/5, 3]
[– 1/5, ∞)
Page 2 of 11
College Algebra MATH 107
Fall, 2017, V3.2
6. Which of the following represents the graph of 9x − 4y = 36 ?
A.
B.
C.
D.
6. ______
Page 3 of 11
College Algebra MATH 107
Fall, 2017, V3.2
7. Write a slope-intercept equation for a line parallel to the line x – 7y = 3 which passes through
the point (28, –5).
7. ______
A.
y=
1
x−9
7
B.
y=
1
x−5
7
C.
y = − 7 x + 191
D.
1
y = − x −1
7
8. Which of the following best describes the graph?
A.
B.
C.
D.
8. ______
It is the graph of a function and it is one-to-one.
It is the graph of a function but not one-to-one.
It is the graph of an absolute value relation.
It is not the graph of a function.
Page 4 of 11
College Algebra MATH 107
9. Express as an equivalent expression: 2 log (x + 3) – 4 log y + log 1
A.
log ( 2 x + 7 − 4 y )
B.
6 log( x)
log(4 y )
C.
 x2 + 9 
log  4 
 y 
D.
 ( x + 3)2 
log 

 y4 


10. Which of the functions corresponds to the graph?
Fall, 2017, V3.2
9. ______
10. ______
A. f ( x ) = 2e − x − 1
B. f ( x ) = e − x + 1
C. f ( x ) = −e x + 2
D. f ( x ) = e − x + 2
Page 5 of 11
College Algebra MATH 107
Fall, 2017, V3.2
11. Suppose that for a function f , the equation f (x) = 0 has no real-number solutions.
Which of the following statements MUST be true?
A.
B.
C.
D.
11. ______
f (x) > 0 for all x in the domain of f.
f is an invertible function.
f has no x-intercepts.
f has no y-intercepts.
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 – 3) – 2
g(x) = f (x – 2) – 3
g(x) = f (x + 3) – 2
g(x) = f (x + 2) – 3
Page 6 of 11
College Algebra MATH 107
Fall, 2017, V3.2
SHORT ANSWER:
13. Multiply and simplify: (8 + i)(5 + 3i).
Write the answer in the form a + bi, where a and b are real numbers.
14. Solve, and write the answer in interval notation:
x+2
≤ 0.
x−5
Answer: ________
Answer: ________
15. A can of soda at 78° F. is placed in a refrigerator that maintains a constant temperature of 35°
F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by
T(t) = 35 + 43e
– 0.058 t
Find the temperature of the soda 12 minutes after it is placed in the refrigerator. (Round to the
nearest tenth of a degree.)
Answer: ________
 1 
16. Find the value of the logarithm: log 5 
.
 125 
17. Solve:
38 x−5 = 9 .
Answer: ________
Answer: ________
18. Suppose $3,400 is invested in an account at an annual interest rate of 6.1% 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 + 8x + 19.
(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
Fall, 2017, V3.2
20. Consider the polynomial P(x), shown in both standard form and factored form.
P ( x) = x3 − 3 x 2 − x + 3 = ( x + 1)( x − 1)( x − 3)
(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) =
Fall, 2017, V3.2
2+ x
.
3− x
(a) State the domain.
Answer: _________________
(b) State the vertical asymptote(s).
Answer: _________________
(c) State the horizontal asymptote.
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
Fall, 2017, V3.2
SHORT ANSWER, with work required to be shown, as indicated.
22. Let f (x) = x – 3 and g ( x) = x + 5 .
f 
(a) Find  (−1) . Show work.
g
(b) Find the domain of the quotient function
f
. Explain.
g
23. Points (1, –5) and (9, –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 (4, 3) and (6, –7). Write the
equation in slope-intercept form. Show work.
25. A salesperson earns a base salary of $2,100 per month and a commission of 6.5% on the
amount of sales made. If the salesperson has a paycheck of $5,168 for one month, what was the
amount of sales for the month? Show work.
26. Let f (x) = 3×2 + 8 and g(x) = x – 4.
(a) Find the composite function ( f o g )( x) and simplify. Show work.
(b) Find ( f o g ) (−1) . Show work.
2
27. Find the exact solutions and simplify as much as possible: 8x = 3 + 8x. Show work.
1
28. Given the function f ( x) = 5 − x , find a formula for the inverse function. Show work.
9
Page 10 of 11
College Algebra MATH 107
Fall, 2017, V3.2
29. The Adventure Travel bus company has determined that when x tourists are given a
particular bus tour, the profit P (in dollars) is given by
P(x) = –0.25 x2 + 25.50x – 220
(a) What is the company’s profit if 32 tourists are given the tour?
(b) How many tourists should be given the tour in order to maximize the company’s profit?
Show work.
30. Solve:
x+5
12
+ 2
= 0 . Show work.
x+2 x −4
Page 11 of 11
…
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