Exam 4: Polynomial and Rational Functions

Classify the polynomial as constant, linear, quadratic, cubic, or quartic, and determine the leading term, the leading coefficient, and the degree of the polynomial. - $f ( x ) = 7 x ^ { 2 } - 10 + 0.12 x - 7 x ^ { 3 }$

(Multiple Choice)

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Question 81

Solve the problem. -The position of an object moving in a straight line is given by $s = 6 t ^ { 2 } - 4 t$ , where $s$ is in meters and $t$ is the time in seconds the object has been in motion. How far will an object move in 20 seconds?

(Multiple Choice)

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Question 82

Match the equation with the appropriate graph. - $f ( x ) = \frac { 2 x ^ { 2 } } { x ^ { 2 } - 4 }$

(Multiple Choice)

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Question 83

Solve the problem. -If there are $x$ teams in a sports league and all the teams play each other twice, a total of $N ( x )$ games are played, where $N ( x ) = x ^ { 2 } - x$ . A soccer league has 6 teams, each of which plays the others twice. If the league pays $\$ 49$ per game for the field and officials, how much will it cost to play the entire schedule?

(Multiple Choice)

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Question 84

Factor the polynomial f(x). Then solve the equation f(x) = 0. - $f ( x ) = x ^ { 3 } + 11 x ^ { 2 } + 36 x + 36$

(Multiple Choice)

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Question 85

Use the leading-term test to match the function with the correct graph. - $f ( x ) = - 0.6 x ^ { 6 } - x ^ { 5 } + 5 x ^ { 4 } - 3 x ^ { 3 } - 6 x ^ { 2 } + x - 3$

(Multiple Choice)

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Question 86

Find the correct end behavior diagram for the given polynomial function. - $f ( x ) = \sqrt { 3 } x ^ { 6 } - x ^ { 5 } + 7 x ^ { 2 } - 4$

(Multiple Choice)

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Question 87

Solve the problem. -Assume that a person's threshold weight $W$ , defined as the weight above which the risk of death rises dramatically, is given by $W ( h ) = \left( \frac { h } { 12.3 } \right) ^ { 3 }$ , where $W$ is in pounds and $h$ is the person's height in inches. Find the threshold weight for a person who is $6 \mathrm { ft } 1$ in. tall. Round your answer to the nearest pound.

(Multiple Choice)

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Question 88

Use substitution to determine whether the given number is a zero of the given polynomial. - $- 3 ; f ( x ) = x ^ { 4 } - 3 x ^ { 2 } - 54$

(Multiple Choice)

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Question 89

Use substitution to determine whether the given number is a zero of the given polynomial. -3; $f ( x ) = - x ^ { 4 } - 8 x ^ { 2 } - 5 x + 168$

(Multiple Choice)

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Question 90

Find the horizontal asymptote, if any, of the rational function. - $f ( x ) = \frac { x ^ { 2 } + 5 x - 7 } { x - 7 }$

(Multiple Choice)

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Question 91

Solve. - $x ^ { 3 } + 10 x ^ { 2 } + 23 x \geq 0$

(Multiple Choice)

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Question 92

Match the equation with the appropriate graph. - $f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } - 4 }$

(Multiple Choice)

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Question 93

Classify the polynomial as constant, linear, quadratic, cubic, or quartic, and determine the leading term, the leading coefficient, and the degree of the polynomial. - $g ( x ) = \frac { 1 } { 2 } x ^ { 3 } - 12 x + 8$

(Multiple Choice)

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Question 94

Classify the polynomial as constant, linear, quadratic, cubic, or quartic, and determine the leading term, the leading coefficient, and the degree of the polynomial. - $f ( x ) = 7 x ^ { 2 } - 10 + 0.12 x - 7 x ^ { 3 }$

Solve the problem. -The position of an object moving in a straight line is given by $s = 6 t ^ { 2 } - 4 t$ , where $s$ is in meters and $t$ is the time in seconds the object has been in motion. How far will an object move in 20 seconds?

Match the equation with the appropriate graph. - $f ( x ) = \frac { 2 x ^ { 2 } } { x ^ { 2 } - 4 }$

Factor the polynomial f(x). Then solve the equation f(x) = 0. - $f ( x ) = x ^ { 3 } + 11 x ^ { 2 } + 36 x + 36$

Use the leading-term test to match the function with the correct graph. - $f ( x ) = - 0.6 x ^ { 6 } - x ^ { 5 } + 5 x ^ { 4 } - 3 x ^ { 3 } - 6 x ^ { 2 } + x - 3$

Find the correct end behavior diagram for the given polynomial function. - $f ( x ) = \sqrt { 3 } x ^ { 6 } - x ^ { 5 } + 7 x ^ { 2 } - 4$

Use substitution to determine whether the given number is a zero of the given polynomial. - $- 3 ; f ( x ) = x ^ { 4 } - 3 x ^ { 2 } - 54$

Use substitution to determine whether the given number is a zero of the given polynomial. -3; $f ( x ) = - x ^ { 4 } - 8 x ^ { 2 } - 5 x + 168$

Find the horizontal asymptote, if any, of the rational function. - $f ( x ) = \frac { x ^ { 2 } + 5 x - 7 } { x - 7 }$

Solve. - $x ^ { 3 } + 10 x ^ { 2 } + 23 x \geq 0$

Match the equation with the appropriate graph. - $f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } - 4 }$

Classify the polynomial as constant, linear, quadratic, cubic, or quartic, and determine the leading term, the leading coefficient, and the degree of the polynomial. - $g ( x ) = \frac { 1 } { 2 } x ^ { 3 } - 12 x + 8$

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Exam 4: Polynomial and Rational Functions

Classify the polynomial as constant, linear, quadratic, cubic, or quartic, and determine the leading term, the leading coefficient, and the degree of the polynomial. - f(x)=7x2−10+0.12x−7x3f ( x ) = 7 x ^ { 2 } - 10 + 0.12 x - 7 x ^ { 3 }f(x)=7x2−10+0.12x−7x3

Solve the problem. -The position of an object moving in a straight line is given by s=6t2−4ts = 6 t ^ { 2 } - 4 ts=6t2−4t , where sss is in meters and ttt is the time in seconds the object has been in motion. How far will an object move in 20 seconds?

Match the equation with the appropriate graph. - f(x)=2x2x2−4f ( x ) = \frac { 2 x ^ { 2 } } { x ^ { 2 } - 4 }f(x)=x2−42x2​

Factor the polynomial f(x). Then solve the equation f(x) = 0. - f(x)=x3+11x2+36x+36f ( x ) = x ^ { 3 } + 11 x ^ { 2 } + 36 x + 36f(x)=x3+11x2+36x+36

Use the leading-term test to match the function with the correct graph. - f(x)=−0.6x6−x5+5x4−3x3−6x2+x−3f ( x ) = - 0.6 x ^ { 6 } - x ^ { 5 } + 5 x ^ { 4 } - 3 x ^ { 3 } - 6 x ^ { 2 } + x - 3f(x)=−0.6x6−x5+5x4−3x3−6x2+x−3

Find the correct end behavior diagram for the given polynomial function. - f(x)=3x6−x5+7x2−4f ( x ) = \sqrt { 3 } x ^ { 6 } - x ^ { 5 } + 7 x ^ { 2 } - 4f(x)=3​x6−x5+7x2−4

Use substitution to determine whether the given number is a zero of the given polynomial. - −3;f(x)=x4−3x2−54- 3 ; f ( x ) = x ^ { 4 } - 3 x ^ { 2 } - 54−3;f(x)=x4−3x2−54

Use substitution to determine whether the given number is a zero of the given polynomial. -3; f(x)=−x4−8x2−5x+168f ( x ) = - x ^ { 4 } - 8 x ^ { 2 } - 5 x + 168f(x)=−x4−8x2−5x+168

Find the horizontal asymptote, if any, of the rational function. - f(x)=x2+5x−7x−7f ( x ) = \frac { x ^ { 2 } + 5 x - 7 } { x - 7 }f(x)=x−7x2+5x−7​

Solve. - x3+10x2+23x≥0x ^ { 3 } + 10 x ^ { 2 } + 23 x \geq 0x3+10x2+23x≥0

Match the equation with the appropriate graph. - f(x)=x3x2−4f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } - 4 }f(x)=x2−4x3​

Classify the polynomial as constant, linear, quadratic, cubic, or quartic, and determine the leading term, the leading coefficient, and the degree of the polynomial. - g(x)=12x3−12x+8g ( x ) = \frac { 1 } { 2 } x ^ { 3 } - 12 x + 8g(x)=21​x3−12x+8

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Classify the polynomial as constant, linear, quadratic, cubic, or quartic, and determine the leading term, the leading coefficient, and the degree of the polynomial. - $f ( x ) = 7 x ^ { 2 } - 10 + 0.12 x - 7 x ^ { 3 }$

Solve the problem. -The position of an object moving in a straight line is given by $s = 6 t ^ { 2 } - 4 t$ , where $s$ is in meters and $t$ is the time in seconds the object has been in motion. How far will an object move in 20 seconds?

Match the equation with the appropriate graph. - $f ( x ) = \frac { 2 x ^ { 2 } } { x ^ { 2 } - 4 }$

Factor the polynomial f(x). Then solve the equation f(x) = 0. - $f ( x ) = x ^ { 3 } + 11 x ^ { 2 } + 36 x + 36$

Use the leading-term test to match the function with the correct graph. - $f ( x ) = - 0.6 x ^ { 6 } - x ^ { 5 } + 5 x ^ { 4 } - 3 x ^ { 3 } - 6 x ^ { 2 } + x - 3$

Find the correct end behavior diagram for the given polynomial function. - $f ( x ) = \sqrt { 3 } x ^ { 6 } - x ^ { 5 } + 7 x ^ { 2 } - 4$

Use substitution to determine whether the given number is a zero of the given polynomial. - $- 3 ; f ( x ) = x ^ { 4 } - 3 x ^ { 2 } - 54$

Use substitution to determine whether the given number is a zero of the given polynomial. -3; $f ( x ) = - x ^ { 4 } - 8 x ^ { 2 } - 5 x + 168$

Find the horizontal asymptote, if any, of the rational function. - $f ( x ) = \frac { x ^ { 2 } + 5 x - 7 } { x - 7 }$

Solve. - $x ^ { 3 } + 10 x ^ { 2 } + 23 x \geq 0$

Match the equation with the appropriate graph. - $f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } - 4 }$

Classify the polynomial as constant, linear, quadratic, cubic, or quartic, and determine the leading term, the leading coefficient, and the degree of the polynomial. - $g ( x ) = \frac { 1 } { 2 } x ^ { 3 } - 12 x + 8$