1. A drama club is planning a bus trip to New York City to see a Broadway play. The cost per person for the bus rental varies inversely to the number of people going on the trip. It will cost $30 per person if 44 people go on the trip. How much will it cost per person if 55 people go on the trip? Round your answer to the nearest cent, if necessary.
A. $48.00
B. $24.00
C. $12.50
D. $33.00
2. Graph the function. xy + 16 = 0
3. Sketch the asymptotes and graph the function y equals start fraction 6 over left parenthesis x minus 2 right parenthesis end fraction plus 4
4. What is the equation of the function y = six over x translated 5 units to the left and 4 units up?
A. y = six over x minus four + 3
B. y = six over x plus five + 4
C.y = six over x minus five + 4
D.y = six over x plus four + 5
5. Find any points of discontinuity for the rational function.
y = x minus eight over x squared plus five times x minus six
A. x = 8
B. x = –1, x = 6
C. x = 1, x = 6
D. x = 1, x = –6
6. Describe the vertical asymptote(s) and hole(s) for the graph of y = x minus six over x squared plus five times x plus six.
A. asymptotes: x = –2, –3 and hole: x = 6
B. asymptotes: x = –2, –3 and no holes
C. asymptotes: x = 2, –3 and hole: x = 6
D. asymptotes: x = –2, 3 and no holes
7. Find the horizontal asymptote of the graph of y = Start Fraction negative 2 x superscript 6 baseline plus 5 x plus 8 over 8 x superscript 6 baseline plus 6 x plus 5 End Fraction
A. y = –one-fourth
B. y = 0
C. y = 1
D. no horizontal asymptote
8. Which of the following is the graph of the rational function?
y equals StartFraction x squared plus 2 x minus 8 over x squared minus 9 EndFraction
9. Simplify the rational expression. State any restrictions on the variable.
t squared plus t minus six over t squared minus nine
A. CE_t minus two over t minus three_img, t ≠ 3, t ≠ –3
B. t plus two over t minus three, t ≠ 3
C. t plus two over t plus three, t ≠ 3, t ≠ –3
D. t plus two over t minus three, t ≠ 3, t ≠ –2
10. What is the product in simplest form? State any restrictions on the variable.
x squared plus five times x plus six over x plus four • x squared plus x minus twelve over x squared plus x minus two
A. parenthesis x plus three parenthesis times parenthesis x minus three parenthesis over x minus one, x ≠ –2, x ≠ –4
B. parenthesis x plus three parenthesis times parenthesis x minus three parenthesis over parenthesis x minus one parenthesis times parenthesis x plus two parenthesis, x ≠ –2, x ≠ –4, x ≠ 1
C. parenthesis x plus three parenthesis times parenthesis x minus three parenthesis over parenthesis x minus one parenthesis times parenthesis x plus two parenthesis, x ≠ –2, x ≠ –4
D. parenthesis x plus three parenthesis times parenthesis x minus three parenthesis over x minus one, x ≠ –2, x ≠ –4, x ≠ 1
11. Which is equivalent to four times x over x minus seven – x plus seven over x?
A. two times x squared plus forty-nine over x times parenthesis x minus seven parenthesis
B. three times x squared plus forty-nine over x times parenthesis x minus seven parenthesis
C. three times parenthesis x plus seven parenthesis over x times parenthesis x minus seven parenthesis
D. three times parenthesis x minus seven parenthesis over x times parenthesis x minus seven parenthesis
12. What is the difference in simplest form?
n squared plus three times n plus two over n squared plus six times n plus eight minus two times n over n plus four
A. one over n plus two
B. one minus n over n plus four
C. three n plus one over n plus four
D. n squared plus two plus two over n squared plus six n plus eight
13. Simplify the sum.
d squared minus seven times d plus twelve over d squared minus d minus six + d squared plus five times d plus six over d squared minus two times d minus fifteen
A. two times d squared minus five times d plus twenty-four over parenthesis d plus two parenthesis times parenthesis minus five parenthesis
B. two times d squared minus thirteen times d plus twenty-four over parenthesis d plus two parenthesis times parenthesis d minus five parenthesis
C. two times d squared plus thirteen times d plus twenty-four over parenthesis d plus two parenthesis times parenthesis d minus five parenthesis
D. two times d squared plus five times d plust twenty-four over parenthesis d plus two parenthesis times parenthesis d minus five parenthesis
14. Simplify the complex fraction.
n minus three over n squared plus six times n plus eight divided by n plus one over n plus two
A. n minus three over parenthesis n plus four parenthesis times parenthesis n plus one parenthesis
B. parenthesis n minus three parenthesis times parenthesis n plus two parenthesis over parenthesis n plus four parenthesis times parenthesis n plus one parenthesis
C. n plus two over parenthesis n plus four parenthesis times parenthesis n plus one parenthesis
D. n minus four over parenthesis n plus four parenthesis times parenthesis n plus one parenthesis
15. Solve the equation. Check the solution.
a over a squared minus sixteen plus two over a minus four equals two over a plus four
A. –16, –4
B. 4
C. –16, 4
D. –16
16. A group of college students is volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Irina can paint a certain room in 8 hours. Paulo can paint the same room in 7 hours. Write an equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room? If necessary, round your answer to the nearest hundredth.
A. Start Fraction 8 over x End Fraction + Start Fraction 7 over lower x End Fraction = 1; 15 hours
B. one-eighth + Start Fraction 1 over 7 End Fraction = Start Fraction 1 over lower x End Fraction; 7.5 hours
C. Start Fraction lower x over 8 End Fraction + start fraction x over 7 end fraction = 1; 3.73 hours
D. Start Fraction lower x over 8 End Fraction+ start fraction x over 7 end fraction= 1; 1.87 hours
1. B. $24.00
4. A. y = six over x minus four + 3
5. B. x = –1, x = 6
6. B. asymptotes: x = –2, –3 and no holes
7. A. y = –one-fourth
9. B. t plus two over t minus three, t ≠ 3
10. C. parenthesis x plus three parenthesis times parenthesis x minus three parenthesis over parenthesis x minus one parenthesis times parenthesis x plus two parenthesis, x ≠ –2, x ≠ –4
11. C. three times parenthesis x plus seven parenthesis over x times parenthesis x minus seven parenthesis
12. C. three n plus one over n plus four
13. A. two times d squared minus five times d plus twenty-four over parenthesis d plus two parenthesis times parenthesis minus five parenthesis
14. B. parenthesis n minus three parenthesis times parenthesis n plus two parenthesis over parenthesis n plus four parenthesis times parenthesis n plus one parenthesis
15. C. –16, 4
16. A. Start Fraction 8 over x End Fraction + Start Fraction 7 over x End Fraction = 1; 15 hours