Download RATIONAL FUNCTIONS I

RATIONAL FUNCTIONS I
Name__________________________________________________Date_____________________
Divide and express the result in standard form.
1)
A)
1) ________
_
B)
2)
2) ________
_
A)
B)
Perform the indicated operations and write the result in standard form.
3)
A)
4) (6 +
B)
) (4 +
4) ________
_
)
A)
B)
Solve the quadratic equation using the quadratic formula. Express the solution in standard form.
5) 7
= 5x - 3
A)
7)
5) ________
_
B)
Find the domain of the rational function.
6)
g(x) =
A)
3) ________
_
6) ________
_
B)
h( =
x)
7)
__
__
__
__
_
A) {
B)
Find the vertical asymptotes, if any, of the graph of the rational function.
8)
g(x) =
A)
8) ________
_
B)
9)
9) ________
_
A)
B)
Find the horizontal asymptote, if any, of the graph of the rational function.
10)
h(x) =
A) y = 3
B)
C)
10) ______
__
D)
y=
11)
g(x) =
A)
Graph the rational function.
12)
11) ______
__
B)
f(x) =
12)
A)
___
___
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B)
13)
13) ______
__
f(x) =
A)
B)
14)
14) ______
__
f(x) = -
A)
B)
Find the slant asymptote, if any, of the graph of the rational function.
15)
f(x) =
A)
B)
15) ______
__
16)
16) ______
__
g(x) =
A)
B)
Solve the problem.
17) A company that produces scooters has costs given by the function
, where x
is the number of scooters manufactured and C(x) is measured in dollars. The average cost to
manufacture each scooter is given by
(x) =
17) ______
__
.
What is the horizontal asymptote for the function
? Describe what this means in practical
terms.
A) y = 20; 20 is the minimum number of scooters the company can produce.
B) y = 20; $20 is the least possible cost for producing each scooter.
C) y = 20,000; 20,000 is the maximum number of scooters the company can produce.
D) y = 20,000; $20,000 is the least possible cost for running the company.
18) A drug is injected into a patient and the concentration of the drug is monitored. The drug's
concentration, C(t), in milligrams after t hours is modeled by
C(t) =
.
What is the horizontal asymptote for this function? Describe what this means in practical terms.
A) y = 1.33; After 1.33 hours, the concentration of the drug is at its greatest.
B) y = 1.33; 1.33 is the final amount, in milligrams, of the drug that will be left in the patient's
bloodstream.
C) y = 0.80; After 0.80 hours, the concentration of the drug is at its greatest.
D) y = 0; 0 is the final amount, in milligrams, of the drug that will be left in the patient's
bloodstream.
18) ______
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1)
2)
3)
4)
5)
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7)
8)
9)
10)
11)
12)
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18)
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D
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B
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B
B
D