Deck 26: Higher Degree Polynomials and Rational Functions

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سؤال
The limiting value of a rational function can be used to find a horizontal asymptote.
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سؤال
A rational function is a function for which the horizontal and vertical asymptotes are the same.
سؤال
What is the horizontal asymptote of the function <strong>What is the horizontal asymptote of the function   ? ​</strong> A)   B)   C)   D)   <div style=padding-top: 35px> ? ​

A) <strong>What is the horizontal asymptote of the function   ? ​</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>What is the horizontal asymptote of the function   ? ​</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>What is the horizontal asymptote of the function   ? ​</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>What is the horizontal asymptote of the function   ? ​</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
What value of x gives the maximum value of the quadratic function <strong>What value of x gives the maximum value of the quadratic function   ? Round your answer to two decimal places. ​</strong> A) 0.70 B) 5.45 C) 1.26 D) 5.78 <div style=padding-top: 35px> ? Round your answer to two decimal places. ​

A) 0.70
B) 5.45
C) 1.26
D) 5.78
سؤال
High-degree polynomials may have many zeros.
سؤال
What value of ​x gives the minimum value of the quadratic function <strong>What value of ​x gives the minimum value of the quadratic function   ? Round your answer to two decimal places. ​</strong> A) 0.63 B) 1.29 C) 3.44 D) 3.51 <div style=padding-top: 35px> ? Round your answer to two decimal places. ​

A) 0.63
B) 1.29
C) 3.44
D) 3.51
سؤال
A rational function is one that always produces rational values.
سؤال
A quadratic function has the form A quadratic function has the form   .<div style=padding-top: 35px> .
سؤال
For <strong>For   , what is the minimum value of the cubic function   ? Round your answer to two decimal places. ​</strong> A) 0.62 B) 3.09 C) 0 D) 6.00 <div style=padding-top: 35px> , what is the minimum value of the cubic function <strong>For   , what is the minimum value of the cubic function   ? Round your answer to two decimal places. ​</strong> A) 0.62 B) 3.09 C) 0 D) 6.00 <div style=padding-top: 35px> ? Round your answer to two decimal places. ​

A) 0.62
B) 3.09
C) 0
D) 6.00
سؤال
A quadratic function is also a polynomial function.
سؤال
A quadratic function always has a limiting value.
سؤال
A rational function is a quotient of polynomial functions.
سؤال
The horizontal asymptote for The horizontal asymptote for   is given by the equation   .<div style=padding-top: 35px> is given by the equation The horizontal asymptote for   is given by the equation   .<div style=padding-top: 35px> .
سؤال
A cubic function may have both a maximum and a minimum.
سؤال
The graph of a quadratic function is a parabola.
سؤال
The amount C, in pounds, of food consumed in a day by a certain grazing animal depends on the amount V, in pounds per acre, of vegetation available.The relationship is given by the rational function <strong>The amount C, in pounds, of food consumed in a day by a certain grazing animal depends on the amount V, in pounds per acre, of vegetation available.The relationship is given by the rational function   What is the most the animal will consume in a day no matter how much vegetation is available? Round your answer to two decimal places, if necessary. ​</strong> A) 4 pounds B) 55 pounds C) 0.07 pounds D) 13.75 pounds <div style=padding-top: 35px> What is the most the animal will consume in a day no matter how much vegetation is available? Round your answer to two decimal places, if necessary. ​

A) 4 pounds
B) 55 pounds
C) 0.07 pounds
D) 13.75 pounds
سؤال
What is the vertical asymptote of the function <strong>What is the vertical asymptote of the function   ? ​</strong> A)   B)   C)   D)   <div style=padding-top: 35px> ? ​

A) <strong>What is the vertical asymptote of the function   ? ​</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>What is the vertical asymptote of the function   ? ​</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>What is the vertical asymptote of the function   ? ​</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>What is the vertical asymptote of the function   ? ​</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
For <strong>For   , what value of x gives the minimum value of the cubic function   ? Round your answer to two decimal places. ​</strong> A) 0.65 B) 1.85 C) 0 D) 4.00 <div style=padding-top: 35px> , what value of x gives the minimum value of the cubic function <strong>For   , what value of x gives the minimum value of the cubic function   ? Round your answer to two decimal places. ​</strong> A) 0.65 B) 1.85 C) 0 D) 4.00 <div style=padding-top: 35px> ? Round your answer to two decimal places. ​

A) 0.65
B) 1.85
C) 0
D) 4.00
سؤال
What value of x gives the minimum value of the quadratic function <strong>What value of x gives the minimum value of the quadratic function   ? Round your answer to two decimal places. ​</strong> A) 2.66 B) 2.44 C) 1.27 D) 0.38 <div style=padding-top: 35px> ? Round your answer to two decimal places. ​

A) 2.66
B) 2.44
C) 1.27
D) 0.38
سؤال
A quartic function may have more than one maximum.
سؤال
The growth rate G, in millions per year, of a certain population depends on the number N, in millions, of individuals present.The relationship is <strong>The growth rate G, in millions per year, of a certain population depends on the number N, in millions, of individuals present.The relationship is   . ​ What is the maximum growth rate of the population? Round your answer to two decimal places. ​</strong> A) 1.29 million per year B) 0.49 million per year C) 0.86 million per year D) 0.15 million per year <div style=padding-top: 35px> . ​
What is the maximum growth rate of the population? Round your answer to two decimal places.

A) 1.29 million per year
B) 0.49 million per year
C) 0.86 million per year
D) 0.15 million per year
سؤال
Use the quadratic formula to write the solution of the quadratic equation <strong>Use the quadratic formula to write the solution of the quadratic equation   . ​</strong> A)   B) ​   C) ​   D) ​   <div style=padding-top: 35px> . ​

A) <strong>Use the quadratic formula to write the solution of the quadratic equation   . ​</strong> A)   B) ​   C) ​   D) ​   <div style=padding-top: 35px>
B) ​ <strong>Use the quadratic formula to write the solution of the quadratic equation   . ​</strong> A)   B) ​   C) ​   D) ​   <div style=padding-top: 35px>
C) ​ <strong>Use the quadratic formula to write the solution of the quadratic equation   . ​</strong> A)   B) ​   C) ​   D) ​   <div style=padding-top: 35px>
D) ​ <strong>Use the quadratic formula to write the solution of the quadratic equation   . ​</strong> A)   B) ​   C) ​   D) ​   <div style=padding-top: 35px>
سؤال
The average number N of prey that certain predators will consume depends on the density D, in number per square foot, of the prey.The relationship is <strong>The average number N of prey that certain predators will consume depends on the density D, in number per square foot, of the prey.The relationship is   . ​ What is the largest average number of prey that predators will consume no matter what the density of the prey is? Round your answer to two decimal places, if necessary. ​</strong> A) 2 B) 6 C) 3.00 D) None of the above <div style=padding-top: 35px> . ​
What is the largest average number of prey that predators will consume no matter what the density of the prey is? Round your answer to two decimal places, if necessary.

A) 2
B) 6
C) 3.00
D) None of the above
سؤال
A ball is tossed upward from the ground.The height H, in feet, of the ball after t seconds is given by <strong>A ball is tossed upward from the ground.The height H, in feet, of the ball after t seconds is given by   . ​ What is the maximum height reached by the ball? Round your answer to two decimal places, if necessary. ​</strong> A) 2.45 feet B) 66.71 feet C) 2.03 feet D) 66.02 feet <div style=padding-top: 35px> . ​
What is the maximum height reached by the ball? Round your answer to two decimal places, if necessary.

A) 2.45 feet
B) 66.71 feet
C) 2.03 feet
D) 66.02 feet
سؤال
A ball is tossed upward from the ground.The height H, in feet, of the ball after t seconds is given by <strong>A ball is tossed upward from the ground.The height H, in feet, of the ball after t seconds is given by   . ​ How long after the ball is tossed will it reach its maximum height? Round your answer to two decimal places. ​</strong> A) 3.76 seconds B) 130.09 seconds C) 2.84 seconds D) 129.39 seconds <div style=padding-top: 35px> . ​
How long after the ball is tossed will it reach its maximum height? Round your answer to two decimal places.

A) 3.76 seconds
B) 130.09 seconds
C) 2.84 seconds
D) 129.39 seconds
سؤال
The growth rate G, in millions per year, of a certain population depends on the number N, in millions, of individuals present.The relationship is <strong>The growth rate G, in millions per year, of a certain population depends on the number N, in millions, of individuals present.The relationship is   . ​ For what population size is the population growing at the fastest rate? Round your answer to two decimal places.</strong> A) 1.46 million B) 1.09 million C) 0.72 million D) 0.13 million <div style=padding-top: 35px> . ​
For what population size is the population growing at the fastest rate? Round your answer to two decimal places.

A) 1.46 million
B) 1.09 million
C) 0.72 million
D) 0.13 million
سؤال
Use the quadratic formula to write the solution of the quadratic equation <strong>Use the quadratic formula to write the solution of the quadratic equation   . ​</strong> A)   B) ​   C) ​   D) ​   <div style=padding-top: 35px> . ​

A) <strong>Use the quadratic formula to write the solution of the quadratic equation   . ​</strong> A)   B) ​   C) ​   D) ​   <div style=padding-top: 35px>
B) ​ <strong>Use the quadratic formula to write the solution of the quadratic equation   . ​</strong> A)   B) ​   C) ​   D) ​   <div style=padding-top: 35px>
C) ​ <strong>Use the quadratic formula to write the solution of the quadratic equation   . ​</strong> A)   B) ​   C) ​   D) ​   <div style=padding-top: 35px>
D) ​ <strong>Use the quadratic formula to write the solution of the quadratic equation   . ​</strong> A)   B) ​   C) ​   D) ​   <div style=padding-top: 35px>
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Deck 26: Higher Degree Polynomials and Rational Functions
1
The limiting value of a rational function can be used to find a horizontal asymptote.
True
2
A rational function is a function for which the horizontal and vertical asymptotes are the same.
False
3
What is the horizontal asymptote of the function <strong>What is the horizontal asymptote of the function   ? ​</strong> A)   B)   C)   D)   ? ​

A) <strong>What is the horizontal asymptote of the function   ? ​</strong> A)   B)   C)   D)
B) <strong>What is the horizontal asymptote of the function   ? ​</strong> A)   B)   C)   D)
C) <strong>What is the horizontal asymptote of the function   ? ​</strong> A)   B)   C)   D)
D) <strong>What is the horizontal asymptote of the function   ? ​</strong> A)   B)   C)   D)
4
What value of x gives the maximum value of the quadratic function <strong>What value of x gives the maximum value of the quadratic function   ? Round your answer to two decimal places. ​</strong> A) 0.70 B) 5.45 C) 1.26 D) 5.78 ? Round your answer to two decimal places. ​

A) 0.70
B) 5.45
C) 1.26
D) 5.78
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5
High-degree polynomials may have many zeros.
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6
What value of ​x gives the minimum value of the quadratic function <strong>What value of ​x gives the minimum value of the quadratic function   ? Round your answer to two decimal places. ​</strong> A) 0.63 B) 1.29 C) 3.44 D) 3.51 ? Round your answer to two decimal places. ​

A) 0.63
B) 1.29
C) 3.44
D) 3.51
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7
A rational function is one that always produces rational values.
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8
A quadratic function has the form A quadratic function has the form   . .
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9
For <strong>For   , what is the minimum value of the cubic function   ? Round your answer to two decimal places. ​</strong> A) 0.62 B) 3.09 C) 0 D) 6.00 , what is the minimum value of the cubic function <strong>For   , what is the minimum value of the cubic function   ? Round your answer to two decimal places. ​</strong> A) 0.62 B) 3.09 C) 0 D) 6.00 ? Round your answer to two decimal places. ​

A) 0.62
B) 3.09
C) 0
D) 6.00
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10
A quadratic function is also a polynomial function.
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11
A quadratic function always has a limiting value.
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12
A rational function is a quotient of polynomial functions.
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13
The horizontal asymptote for The horizontal asymptote for   is given by the equation   . is given by the equation The horizontal asymptote for   is given by the equation   . .
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14
A cubic function may have both a maximum and a minimum.
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15
The graph of a quadratic function is a parabola.
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16
The amount C, in pounds, of food consumed in a day by a certain grazing animal depends on the amount V, in pounds per acre, of vegetation available.The relationship is given by the rational function <strong>The amount C, in pounds, of food consumed in a day by a certain grazing animal depends on the amount V, in pounds per acre, of vegetation available.The relationship is given by the rational function   What is the most the animal will consume in a day no matter how much vegetation is available? Round your answer to two decimal places, if necessary. ​</strong> A) 4 pounds B) 55 pounds C) 0.07 pounds D) 13.75 pounds What is the most the animal will consume in a day no matter how much vegetation is available? Round your answer to two decimal places, if necessary. ​

A) 4 pounds
B) 55 pounds
C) 0.07 pounds
D) 13.75 pounds
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17
What is the vertical asymptote of the function <strong>What is the vertical asymptote of the function   ? ​</strong> A)   B)   C)   D)   ? ​

A) <strong>What is the vertical asymptote of the function   ? ​</strong> A)   B)   C)   D)
B) <strong>What is the vertical asymptote of the function   ? ​</strong> A)   B)   C)   D)
C) <strong>What is the vertical asymptote of the function   ? ​</strong> A)   B)   C)   D)
D) <strong>What is the vertical asymptote of the function   ? ​</strong> A)   B)   C)   D)
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18
For <strong>For   , what value of x gives the minimum value of the cubic function   ? Round your answer to two decimal places. ​</strong> A) 0.65 B) 1.85 C) 0 D) 4.00 , what value of x gives the minimum value of the cubic function <strong>For   , what value of x gives the minimum value of the cubic function   ? Round your answer to two decimal places. ​</strong> A) 0.65 B) 1.85 C) 0 D) 4.00 ? Round your answer to two decimal places. ​

A) 0.65
B) 1.85
C) 0
D) 4.00
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19
What value of x gives the minimum value of the quadratic function <strong>What value of x gives the minimum value of the quadratic function   ? Round your answer to two decimal places. ​</strong> A) 2.66 B) 2.44 C) 1.27 D) 0.38 ? Round your answer to two decimal places. ​

A) 2.66
B) 2.44
C) 1.27
D) 0.38
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20
A quartic function may have more than one maximum.
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21
The growth rate G, in millions per year, of a certain population depends on the number N, in millions, of individuals present.The relationship is <strong>The growth rate G, in millions per year, of a certain population depends on the number N, in millions, of individuals present.The relationship is   . ​ What is the maximum growth rate of the population? Round your answer to two decimal places. ​</strong> A) 1.29 million per year B) 0.49 million per year C) 0.86 million per year D) 0.15 million per year . ​
What is the maximum growth rate of the population? Round your answer to two decimal places.

A) 1.29 million per year
B) 0.49 million per year
C) 0.86 million per year
D) 0.15 million per year
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22
Use the quadratic formula to write the solution of the quadratic equation <strong>Use the quadratic formula to write the solution of the quadratic equation   . ​</strong> A)   B) ​   C) ​   D) ​   . ​

A) <strong>Use the quadratic formula to write the solution of the quadratic equation   . ​</strong> A)   B) ​   C) ​   D) ​
B) ​ <strong>Use the quadratic formula to write the solution of the quadratic equation   . ​</strong> A)   B) ​   C) ​   D) ​
C) ​ <strong>Use the quadratic formula to write the solution of the quadratic equation   . ​</strong> A)   B) ​   C) ​   D) ​
D) ​ <strong>Use the quadratic formula to write the solution of the quadratic equation   . ​</strong> A)   B) ​   C) ​   D) ​
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23
The average number N of prey that certain predators will consume depends on the density D, in number per square foot, of the prey.The relationship is <strong>The average number N of prey that certain predators will consume depends on the density D, in number per square foot, of the prey.The relationship is   . ​ What is the largest average number of prey that predators will consume no matter what the density of the prey is? Round your answer to two decimal places, if necessary. ​</strong> A) 2 B) 6 C) 3.00 D) None of the above . ​
What is the largest average number of prey that predators will consume no matter what the density of the prey is? Round your answer to two decimal places, if necessary.

A) 2
B) 6
C) 3.00
D) None of the above
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24
A ball is tossed upward from the ground.The height H, in feet, of the ball after t seconds is given by <strong>A ball is tossed upward from the ground.The height H, in feet, of the ball after t seconds is given by   . ​ What is the maximum height reached by the ball? Round your answer to two decimal places, if necessary. ​</strong> A) 2.45 feet B) 66.71 feet C) 2.03 feet D) 66.02 feet . ​
What is the maximum height reached by the ball? Round your answer to two decimal places, if necessary.

A) 2.45 feet
B) 66.71 feet
C) 2.03 feet
D) 66.02 feet
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25
A ball is tossed upward from the ground.The height H, in feet, of the ball after t seconds is given by <strong>A ball is tossed upward from the ground.The height H, in feet, of the ball after t seconds is given by   . ​ How long after the ball is tossed will it reach its maximum height? Round your answer to two decimal places. ​</strong> A) 3.76 seconds B) 130.09 seconds C) 2.84 seconds D) 129.39 seconds . ​
How long after the ball is tossed will it reach its maximum height? Round your answer to two decimal places.

A) 3.76 seconds
B) 130.09 seconds
C) 2.84 seconds
D) 129.39 seconds
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26
The growth rate G, in millions per year, of a certain population depends on the number N, in millions, of individuals present.The relationship is <strong>The growth rate G, in millions per year, of a certain population depends on the number N, in millions, of individuals present.The relationship is   . ​ For what population size is the population growing at the fastest rate? Round your answer to two decimal places.</strong> A) 1.46 million B) 1.09 million C) 0.72 million D) 0.13 million . ​
For what population size is the population growing at the fastest rate? Round your answer to two decimal places.

A) 1.46 million
B) 1.09 million
C) 0.72 million
D) 0.13 million
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27
Use the quadratic formula to write the solution of the quadratic equation <strong>Use the quadratic formula to write the solution of the quadratic equation   . ​</strong> A)   B) ​   C) ​   D) ​   . ​

A) <strong>Use the quadratic formula to write the solution of the quadratic equation   . ​</strong> A)   B) ​   C) ​   D) ​
B) ​ <strong>Use the quadratic formula to write the solution of the quadratic equation   . ​</strong> A)   B) ​   C) ​   D) ​
C) ​ <strong>Use the quadratic formula to write the solution of the quadratic equation   . ​</strong> A)   B) ​   C) ​   D) ​
D) ​ <strong>Use the quadratic formula to write the solution of the quadratic equation   . ​</strong> A)   B) ​   C) ​   D) ​
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