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WorksheetsGraphing and Solving Rational equations
Total questions: 88
Worksheet time: 9hrs 41mins
Name
Class
Date
1.
Find the domain of the rational function f(x) = x / (x2-25)
a)
(- infinity, -5) U (5, infinity)
b)
(-infinity, -5) U (-5, 5) U (5, infinity)
c)
(- infinity, 5) U (5, infinity)
d)
(- infinity, 25) U (25, infinity)
2.
Determine the x-coordinate of the hole on the graph of
f(x)= (x2-2x + 1)/(x2+2x - 3)
f(x)= (x2-2x + 1)/(x2+2x - 3)
a)
-1
b)
3
c)
1
d)
-3
3.
State the vertical asymptotes:
f(x) = 2 / (2x2+3x - 5)
f(x) = 2 / (2x2+3x - 5)
a)
x = 1 , x = -5
b)
x = 1, x = -5/2
c)
x = -1/2, x = 5
d)
x = 0 , x = -5/2
4.
Which asymptote(s) are determined by looking at the denominator?
a)
vertical
b)
horizontal
c)
end behavior
d)
none
5.
The y-intercepts of a rational function are:
a)
the value of f(0)
b)
the real zeros of the numerator
c)
always zero
d)
the real zeros of the denominatior
6.
Name any holes of the function.
a)
x=0
b)
none
c)
x=3
d)
x=-3
7.
Solve and check for extraneous solutions.
a)
x=-1, x=-3 extraneous
b)
x=-1 extraneous, x=-2
c)
x=-1, x=-2 extraneous
d)
x=-1, x=2 extraneous
8.
What did the math teacher feed her baby?
a)
square roots
b)
diapers
c)
graph paper
d)
quadratic formula
9.
Solve and check for extraneous solutions.
a)
x=2, not extraneous
b)
x=-2, not extraneous
c)
x=11, extraneous
d)
x=22, extraneous
10.
Solve
a)
A
b)
B
c)
C
d)
D
11.
Match the graph to the correct rational equation below.
a)
f(x)=-8/(x+2) + 2
b)
f(x)=8/(x-2) + 2
c)
f(x)=1/(x+2) + 2
d)
f(x)=-1/(x+2) - 2
12.
a)
All Reals Except 0
b)
All Reals
c)
All Reals Except -3
d)
All Reals Except 0 and -3
13.
What are the asymptotes?
a)
x=-1 y = -3
b)
x=1 y = -3
c)
x=-1 y =3
d)
x=1, y=3
14.
Write an equation of a rational function that has a V.A. at x = 5, and an x- intercept of (3, 0).
a)
y= (x-3) / (x-5)
b)
y= (x+3) / (x+5)
c)
y= (x+3) / (x-5)
d)
y= (x-3) / (x+5)
15.
Find the vertical asymptote(s).
a)
None
b)
x = 0
c)
x= 4
d)
x = -4, 4
16.
What is the horizontal asymptote?
a)
x = 2
b)
y = 2
c)
x = 1
d)
y = 1
17.
How is this function transformed from the parent function?
a)
Translated left and up
b)
Translated right and up
c)
Translated left and down
d)
Translated right and down
18.
What are the asymptotes?
a)
x=-3, y=1
b)
x=3, y =1
c)
x=-3, y =-1
d)
x=3 y=-1
19.
What is the parent function of a rational function?
a)
Y=X²
b)
Y=X
c)
1 / X
d)
Y=X / 1
20.
State the vertical asymptote: f(x)=(x-2)/(x+5).
a)
x = -2/5
b)
x = -5/2
c)
x = -5
d)
x = 2
21.
a)
-1
b)
0
c)
4
d)
None
22.
What are the asymptotes of the following function:
y = x / (2x - 6)
y = x / (2x - 6)
a)
y = 1/2, x = 3
b)
y = 2, x = 6
c)
y = 1/2, x = 6
d)
y = 2, x = 3
23.
What is the y-intercept for f(x) = (2x - 18)/(2x + 6)
a)
(-9,0)
b)
(-3,0)
c)
(0,-3)
d)
(0,1)
24.
a)
A
b)
B
c)
C
d)
D
25.
a)
A
b)
B
c)
C
d)
D
26.
What is the horizontal asymptote?
a)
x = 2
b)
x = 7
c)
y = 2
d)
y = 7
27.
What is the vertical asymptote?
a)
x = 2
b)
x = 7
c)
y = 2
d)
y = 7
28.
a)
A
b)
B
c)
C
d)
D
29.
Which equation represents this graph?
a)
R(x) = -3 /((x-1)(x+5))
b)
R(x) = -3/ ((x+1)(x-5))
c)
R(x) = 1/ (x-1)(x+5)
30.
Which Equation does this graph represent?
a)
(x-3)/
((x+4)(x-2)^2)
((x+4)(x-2)^2)
b)
(x-3)/
(x+4)^2 (x-2)
(x+4)^2 (x-2)
c)
(x-3)/
(x+4)(x-2)
(x+4)(x-2)
31.
Solve for v
a)
- 7/6
b)
- 9/5
c)
9/5
d)
-3
32.
Solve for x
a)
5
b)
4/5
c)
1
d)
- 4
33.
Solve
a)
11
b)
5
c)
8
d)
7
34.
Solve
a)
A
b)
B
c)
C
d)
D
35.
solve
a)
-3
b)
3
c)
4
d)
-4
36.
this common denominator will have the factors 3 and x
a)
2
b)
18/5
c)
26/5
d)
6
37.
Tim can paint the football field in 8 hours. JaQuii can paint the football field in 6 hours. Damien can paint the field in 4 hours. How long does it take them to paint the field together?
a)
It will take them 24 hours.
b)
It will take them 1.8 hours.
c)
It will take them 11 hours.
d)
It will take them 2.4 hours.
38.
solve
a)
x = 6, -3
b)
x = 6
c)
x = -3
d)
x = -6, 3
39.
solve
a)
x = 10
b)
x = -30/13
c)
x = 6
d)
no solution
40.
Fran can clean the garage in 3 hours, but it takes Angie 4 hours to do the same job. How long would it take them to clean the garage if they worked together?
a)
1.7 hours
b)
1.9 hours
c)
2.1 hours
d)
2.3 hours
41.
After a heavy snowfall, Brian can shovel all of the driveway in 30 minutes. If his younger brother Allen helps, the job takes only 20 minutes. How long would it take Allen to do the job by himself?
a)
60 minutes
b)
45 minutes
c)
50 minutes
d)
555 minutes
42.
a)
x = 3
b)
x = 1
c)
x = -3
d)
x = -2
43.
a)
x = 1, x = -3
b)
x = -4
c)
x = 1
d)
x= -4, x = -3
44.
What is the Vertical Asymptote?
a)
x= 0
b)
x= 4
c)
x= 5
d)
x= -5
45.
The function has a hole at
a)
x = 1
b)
x = -1
c)
y = 1
d)
y = -1
46.
Simplify.
a)
(x+6)/(x+4)
b)
(x+6)(x+4)
c)
(x+6)
d)
(x+6)/(x-5)
47.
Simplify.
a)
(m+6)/(m-3)
b)
7/(m-3)
c)
7(m+6)
d)
(m-3)
48.
Simplify.
a)
1/(n-7)
b)
n-7
c)
(n-6)/(n-7)
d)
n-6
49.
Simplify.
a)
(x+6)/(x+4)
b)
(x+6)(x+4)
c)
(x+6)
d)
(x+6)/(x-5)
50.
Find the least common denominator of the expression
a)
18
b)
6x
c)
3xy
d)
6xy
51.
Simplify the expression
a)
(5x + 4y) / 9y
b)
(6y + 3x) / 3y
c)
(2y + x) / y
d)
(6y + 3x) / 9y
52.
Simplify the expression
a)
n / 2m
b)
n / 3m
c)
(m2 + 4n2) / 12m
d)
n / 4m
53.
Simplify the expression
a)
(-17x - 12y) / 15x
b)
(23x - 4y) / 15x
c)
(-17x - 4y) / 15x
d)
(-3x - 4y) / 8x
54.
Multiply and Simplify
a)
4(x+3)/(x+2),
b)
(x+2)/4(x+1)
c)
(x+2)/4(x+3),
d)
4(x+1)/(x+2),
55.
Simplify.
a)
A
b)
B
c)
C
d)
D
56.
Simplify and state the excluded values.
a)
A
b)
B
c)
C
d)
D
57.
Solve
a)
x = 0 , 4
b)
x = 1 , 3
c)
x = -4 , 0
d)
x = 5 , 2
58.
Solve for r
a)
5
b)
- 5, 4
c)
- 5
d)
5, 4
59.
Simplify and state the excluded values.
a)
A
b)
B
c)
C
d)
D
60.
Simplify.
a)
A
b)
B
c)
C
d)
D
61.
Simplify and state the excluded values.
a)
A
b)
B
c)
C
d)
D
62.
Simplify and state the excluded values.
a)
A
b)
B
c)
C
d)
D
63.
Simplify and state the excluded values.
a)
A
b)
B
c)
C
d)
D
64.
Divide and Simplify
a)
A
b)
B
c)
C
d)
D
65.
Subtract the fractions
a)
a
b)
b
c)
c
d)
d
66.
Add the fractions
a)
a
b)
b
c)
c
d)
d
67.
Peter can mow the lawn in 40 minutes and John can mow the lawn in 60 minutes. How long will it take for them to mow the lawn together?
a)
48 minutes
b)
50 minutes
c)
24 minutes
d)
12 minutes
68.
Igor can do a job in 20 minutes. Fred can do the same job in 30 minutes. How long will the job take if they both work together?
a)
15 minutes
b)
22 minutes
c)
25 minutes
d)
12 minutes
69.
Solve by using the LCD.
a)
x = 4/3
b)
x = 2
c)
x = 3/4
d)
x = 2/3
70.
Lucy and Quinn have started a car washing business. Lucy can wash a car in 3 hours. Together, Lucy and Quinn can wash a car in 1 hour. How long does it take Quinn to wash a car by herself?
a)
It takes Quinn 4 hours.
b)
It takes Quinn 2 hours.
c)
It takes Quinn 1.5 hours.
d)
I don't know. It's too cold to wash cars! *DON'T PICK THIS!*
71.
Tim can paint the football field in 8 hours. JaQuii can paint the football field in 6 hours. Damien can paint the field in 4 hours. How long does it take them to paint the field together?
a)
It will take them 24 hours.
b)
It will take them 1.8 hours.
c)
It will take them 11 hours.
d)
It will take them 2.4 hours.
72.
Find the LCD of these fractions.
a)
(x+2)(x-1)x
b)
+2, -1
c)
(x+1)(x-2)
d)
(x+2)(x-1)
73.
Find the LCD of these fractions.
a)
3x
b)
9x
c)
x
d)
18x
74.
Find the LCD of these fractions.
a)
x2
b)
2x
c)
2x2
d)
x
75.
Find the LCD of these fractions.
a)
(x+2)(x-2)
b)
(x+2)
c)
(x-2)
d)
(x2-4)(x+2)
76.
Find the LCD of these fractions.
a)
(x+1)(x-5)
b)
(x+1)(x-3)
c)
(x-3)(x-5)
d)
(x+1)(x-5)(x-3)
77.
What is the distance formula?
a)
D=R/T
b)
D=T/R
c)
D=R*T
d)
Uhhh...
78.
What is the rate formula?
a)
R=D/T
b)
R=D*T
c)
R=T/D
d)
We did not learn this
79.
How many liters of a 15% sugar solution must be mixed with 5 liters of a 40% sugar solution to make a 30% sugar solution?
a)
250 L
b)
25 L
c)
10/3 L
d)
15 L
80.
Ms. Delgado found a speical on t-shirts with catchy math phrases. The store charges $20 to create the design and $12 per shirt. Find the number of teachers needed to have the average cost per teacher be $14.
a)
10
b)
2
c)
20
d)
15
81.
Liberty is publishing a calendar to raise money. It costs $650 to create the design and $4.50 to print each calendar. How many calendars must be sold for the average cost per calendar to be $8?
a)
186
b)
180
c)
143
d)
190
82.
It costs $100 to rent out JumpStreet for a party and $3 per person attending the party. Write an equation that would be used to find the number of people needed to have the cost per person to be $7.
a)
(100 + 3x) / x = 7
b)
100 + 3x = 7 / x
c)
(100x + 3) / x = 7
d)
(100 + 3x) / 3x = 7
83.
a)
6 hours
b)
3 hours
c)
2 hours
d)
4 hours
84.
A newborn baby weighs approximately 123 ounces at birth. The baby gains approximately 6 ounces per week. How many weeks will it take for the baby to weigh 141 ounces?
a)
20.5 weeks
b)
3 weeks
c)
2 weeks
d)
23.5 weeks
85.
A taxi ride costs an initial fee of $4 plus $1.25 for every mile driven. How many miles will a person travel if they have $29?
a)
6 miles
b)
7 miles
c)
23 miles
d)
20 miles
86.
a)
.75 mph
b)
5 mph
c)
4.7 mph
d)
2.5 mph
87.
Ricky paddles his canoe at a rate of 8 miles per hour in still water. Last weekend he canoed on
Carver Creek going downstream with the current for 5 miles and then returning upstream against the
current. If the trip took him 4 hours to complete, what was the speed of the current?
a)
2.4 mph
b)
4.5 mph
c)
5 mph
d)
not here
88.
An 8-man rowing crew rows at a speed of 10 miles per hour in still water. Every morning they practice
by rowing 4 miles upstream and then 4 miles downstream. If it takes them 5/6
6
of an hour to complete
the trip, what is the speed of the current?
a)
1 mph
b)
2 mph
c)
3 mph
d)
4 mph
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