Rational Functions Unit Test
Erica Hutcheson is taking this assessment.
This assessment was assigned 0 points by Jessica Coleman. Once taken, the actual score will be used
instead.
Multiple Choice
1. Suppose that y varies jointly with w and x and inversely with z and y = 400 when w = 10, x =
25, and z = 5. Write the equation that models the relationship.
(1 point)
y=
y=
y=
y=
2. A drama club is planning a bus trip to New York City to see a Broadway play. The cost per
(1 point)
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 60 people go on
the trip? Round your answer to the nearest cent, if necessary.
$22.00
$40.91
$1,320.00
$21.29
3. Graph the function. (1 point)
xy + 16 = 0
4.
Sketch the asymptotes and graph the function
(1 point)
5. What is the equation of the function y =
translated 4 units to the left and 3 units up? (1 point)
6. Find any points of discontinuity for the rational function. (1 point)
y=
x=8
x = –1, x = 6
x = 1, x = 6
x = 1, x = –6
7. Describe the vertical asymptote(s) and hole(s) for the graph of
asymptotes: x = –3, –1 and no holes.
asymptote: x = –3 and hole: x = –5
asymptotes: x = –3, –1 and hole: x = –5
asymptote: x = –5 and hole: x = –3
y=
.
(1 point)
8. Find the horizontal asymptote of the graph of =
y
(1 point)
y=–
y=0
y=1
no horizontal asymptote
9. Which of the following is the graph of the rational function? (1 point)
10. Simplify the rational expression. State any restrictions on the variable. (1 point)
, t ≠ 3, t ≠ –3
,t≠3
, t ≠ 3, t ≠ –3
, t ≠ 3, t ≠ –2
11. What is the product in simplest form? State any restrictions on the variable. (1 point)
•
(1 point)
•
, x ≠ –3, x ≠ –4
, x ≠ –3, x ≠ –4, x ≠ 1
, x ≠ –3, x ≠ –4, x ≠ 1
, x ≠ –3, x ≠ –4
12. Which is equivalent to
–
? (1 point)
13. What is the difference in simplest form? (1 point)
–
14. Simplify the sum.
+
(1 point)
(1 point)
+
15. Simplify the complex fraction. (1 point)
16. Solve the equation. Check the solution. (1 point)
+
=
–9
–6
–9 and –6
6
17. A group of college students is volunteering for Help the Homeless during their spring break.
(1 point)
17. 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.
+
= 1; 15 hours
+
=
+
= 1; 3.73 hours
+
(1 point)
; 3.73 hours
= 1; 1.87 hours
Essay
Note: Your teacher will review your response to ensure you receive proper credit for your answer.
18. Does the relation in the table represent direct variation, inverse variation, or neither? If it is
direct or inverse variation, write an equation to represent the relation. Explain your answer.
19.
x
5
10
y
2
1
15
20
(3 points)
(2 points)
WorkPad
Note: Remember to show all steps that you use to solve the problem. You can use the
comments field to explain your work. Your teacher will review each step of your response to
ensure you receive proper credit for your answer.
Suppose c and d vary inversely, and d = 2 when c = 17.
a.
Write an equation that models the variation.
b.
Find d when c = 68.
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What is the quotient in simplest form? State any restrictions on the variable.
(6 points)
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Describe the graph of
compared to the graph of
.
(3 points)
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