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1.
Determine which one of the following functions is a power function.
A)
–4 – 5yx=
B)
2
57yx=+
C)
( )
9 3.1 x
y=
D)
4
14yx=
2.
For the power function below identify A) k and B) p.
3.
Given that y is directly proportional to x and
17.1y=
when
3x=
, find a formula to
describe the relationship.
4.
Given that y is directly proportional to x, and
3.9y=
when
3x=
, find y when
4x=
.
5.
Given that y is directly proportional to x, and
49y=
when
5x=
,
A) find a general formula to describe the relationship, and
B) use the formula to find y when
4x=
.
6.
Given that y is directly proportional to the cube root of x, and
26.01y=
when
1.7x=
,
find a formula to describe the relationship.
Write your answer in the form
p
y kx=
.
7.
Given that y is directly proportional to the square of x, and
55.296y=
when
2.4x=
,
the formula
p
y kx=
describes this relationship.
Find A) p and B) k.
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8.
Given that y is directly proportional to the square root of x, and
28y=
when
16x=
,
the formula
p
y kx=
describes this relationship.
Find p and k.
A)
p is 19.5 and k is 15.21
B)
p is 5 and k is 1/2
C)
p is 15.21 and k is 19.5
D)
p is 1/2 and k is 5
9.
Given that y is directly proportional to the cube of x, and
9.2y=
when
97.336x=
,
find y when
8x=
.
Round to two decimal places, if necessary.
10.
Given that y is directly proportional to the square of x, and
10.24y=
when
1.6x=
,
A) find a formula to describe the relationship (Write your answer in the form
p
y kx=
)
and,
B) use the formula to find y when
3x=
. Round your answer to 2 decimal places, if
necessary.
11.
The cost, C, of a diamond is directly proportional to the square of its weight, w (in
carats).
A 0.5-carat diamond costs 2,250 dollars.
A) Find a general formula to describe the relationship, (Write your answer in the form
p
C kw=
), and
B) use the formula to find the cost, in dollars, of a 3.5-carat diamond.
12.
The cost, C, of a diamond is directly proportional to the square of its weight, w (in
carats).
If a 1-carat diamond costs 8,500 dollars, find the cost, in dollars, of a 4-carat diamond.
13.
If y is directly proportional to the cube of x, by what factor does y change when x
triples?
A)
1/ 2
2
B)
3
C)
2
2
D)
1/3
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14.
If w is jointly proportional to the square root of x and to the square of y, and
192w=
when
27x=
and
4y=
, then find a general formula to describe the relationship. Use
fractional exponents rather than radicals, if necessary.
15.
If w is jointly proportional to the square of x and to y, and
144w=
when
216x=
and
4y=
, then find w when
3x=
and
10y=
. Round your answer to 2 decimal
places, if necessary.
16.
If w is jointly proportional to the cube of x and to the cube of y, and
10800w=
when
6x=
and
25y=
, then
A) find a general formula to describe the relationship (use fractional exponents rather
than radicals, if necessary) and,
B) use the formula to find w when
5x=
and
9y=
. Round your answer to 2 decimal
places, if necessary.
17.
The cost, C, of copper tubing is jointly proportional to the length, l, of the pipe and the
square of the diameter, d, of the pipe.
A 32-inch length of 1-inch diameter copper tubing costs $48.00.
A) Find a general formula to describe the relationship, and
B) use the formula to find the cost, in dollars, of a 44-inch length of 1.5-inch diameter
copper pipe.
Round your answer to 2 decimal places, if necessary.
18.
Evaluate the following function when x = –2.
4
( ) –7f x x=
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Answer Key