# Solutions4324

College Algebra MATH 107
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 [–3, 3]; Range [–2, 4]
B. Domain [–3, 3/2]; Range [3/2, 4]
C. Domain [–2, 4]; Range [–3, 3]
D. Domain [0, 3]; Range [–3, 3]
3. Determine the interval(s) on which the function is decreasing. 3. ______
4. Determine whether the graph of
7y x-= 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:
6. Which of the following represents the graph of 9x – 4y = 36 ? 6. ______
College Algebra MATH 107 Spring, 2018, V3.1
7. Write a slope-intercept equation for a line parallel to the line x – 8y = 16 which passes through
the point (24, –1). 7. ______
8. Which of the following best describes the graph? 8. ______
A. It is an absolute value relation.
B. It is not the graph of a function.
C. It is the graph of a function but not one-to-one
D. It is the graph of a function and it is one-to-one.
9. Express as a single logarithm: log x – 6 log y + log 1 9. ______
6
10. Which of the functions corresponds to the graph? 10. ______
College Algebra MATH 107 Spring, 2018, V3.1
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? 11. ______
A. f (x) > 0 for all x in the domain of f.
B. f has no x-intercepts.
C. f has no y-intercepts.
D. f is an invertible 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. ______
13. Multiply and simplify: (3 + 5i)(5 – 4i).
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:
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.)
16. Find the value of the logarithm:
1
log
3
9
17. Solve:
7 2
x-
6 36
18. Suppose \$9,200 is invested in an account at an annual interest rate of 5.7% compounded
continuously. How long (to the nearest tenth of a year) will it take the investment to double in
19. Let f (x) = x
2
+ 8x + 9.
(a) Find the vertex. Answer: ________
(b) State the range of the function. Answer: ________
(c) On what interval is the function decreasing? Answer: ________
Page 7 of 11
College Algebra MATH 107 Spring, 2018, V3.1
20. Consider the polynomial P(x), shown in both standard form and factored form.
1 1 7 41 1
( ) 3 ( 3)( 1)( 2)( 5)
4 3 2
P x x x x x x x x x= – – + + + = – – + + +
(a) Which sketch illustrates the end behavior of the polynomial function?
10 2 10 10 10
(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 B
A.
B. C. D.
GRAPH C GRAPH D
Page 8 of 11
College Algebra MATH 107 Spring, 2018, V3.1
21. Let
(a) State the domain. Answer: _________________
(b) State the horizontal asymptote. Answer: _________________
(c) State the vertical asymptote(s).
(d) Which of the following represents the graph of
GRAPH A. GRAPH B.
GRAPH C. GRAPH D.
Page 9 of 11
College Algebra MATH 107 Spring, 2018, V3.1
SHORT ANSWER, with work required to be shown, as indicated.
22. Let
5)( += xxf and g(x) = x – 7.
(a) Find )1(-
Show work.
(b) Find the domain of the quotient function
23. Points (–1, 0) and (–9, –8) 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 y-axis.
24. Find the equation for a line which passes through the points (6, –3) and (2, 9). Write the
equation in slope-intercept form.
Show work.
25. Bill, a resident of Metropolis, pays Metropolis an annual tax of \$50 plus 1.8% of his annual
income. If Bill paid \$1,526 in tax, what was Bill’s income?
Show work.
26. Let f (x) = 7x
2
+ 5 and g(x) = x – 5.
(a) Find the composite function ))(( xgf ο and simplify. Show work.
(b) Find
( )
(2)f go . Show work.
27. Find the exact solutions and simplify as much as possible:
3x
2
+2 = 6x. Show work.
28. Given the function
1
( ) 6
7
f x x= – , find a formula for the inverse function. Show work.
Page 10 of 11
College Algebra MATH 107 Spring, 2018, V3.1
29. The Travel Time 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 x
2
+ 29.50x – 280
(a) What is the company’s profit if 46 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:
10 32