Find the cubic or quartic function that models the data in the table. -\[\begin{array} { c | c c c c c } \mathrm { x } & 2 & 3 & 5 & 6 & 7 \\ \hline \mathrm { y } & 3 & 5 & 9 & 15 & 19 \end{array} \text { (Quartic) }\]

A) $y = - 0.18 x ^ { 4 } + 3.27 x ^ { 3 } - 20.02 x ^ { 2 } + 51.93 x - 44.00$ B) $y = 0.16 x ^ { 4 } + 3.77 x ^ { 3 } + 20.02 x ^ { 2 } + 51.93 x - 44.00$ C) $y = - 0.18 x ^ { 4 } + 3.27 x ^ { 3 } + 20.02 x ^ { 2 } + 55.93 x - 46.00$ D) $y = - 0.18 x ^ { 4 } + 3.77 x ^ { 3 } - 20.02 x ^ { 2 } + 41.93 x - 44.00$ A) $y = - 0.18 x ^ { 4 } + 3.27 x ^ { 3 } - 20.02 x ^ { 2 } + 51.93 x - 44.00$ B) $y = 0.16 x ^ { 4 } + 3.77 x ^ { 3 } + 20.02 x ^ { 2 } + 51.93 x - 44.00$ C) $y = - 0.18 x ^ { 4 } + 3.27 x ^ { 3 } + 20.02 x ^ { 2 } + 55.93 x - 46.00$ D) $y = - 0.18 x ^ { 4 } + 3.77 x ^ { 3 } - 20.02 x ^ { 2 } + 41.93 x - 44.00$

Exam 6: Higher-Degree Polynomial and Rational Functions

Photon Lighting Company determines that the supply and demand functions for its most popular lamp are as follows: $S ( p ) = 300 - 3 p + 0.000015 p ^ { 4 } \text { and } D ( p ) = 2100 - 0.0009 p ^ { 3 }$ , where p is the price. Determine the price for which The supply equals the demand.

(Multiple Choice)

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Question 101

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - $- 3 x ^ { 4 } + 12 x ^ { 3 } + 3 x ^ { 2 } - 48 x + 36 = 0 ; 2$

(Multiple Choice)

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Question 102

Solve the polynomial equation. - $( 3 x + 1 ) ( x - 2 ) ^ { 2 } ( x + 6 ) = 0$

(Multiple Choice)

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Question 103

Determine all possible rational solutions of the polynomial equation. - $f ( x ) = 11 x ^ { 3 } + 19 x ^ { 2 } + 2 x - 22$

(Multiple Choice)

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Question 104

Find one solution graphically and then find the remaining solutions using synthetic division. - $x ^ { 3 } - 4 x ^ { 2 } - 36 x + 144 = 0$

(Multiple Choice)

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Question 105

$\frac { - 6 x + 2 } { 6 x ^ { 2 } + 6 } > 0$

(Multiple Choice)

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Question 106

The profit function for a product is given by $P ( x ) = - 0.7 x ^ { 3 } + 115.5 x ^ { 2 } - 3710 x - 84,000$ dollars, where x is the number of units produced and sold. Determine the levels of production and sale that give break-even.

(Multiple Choice)

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Question 107

A company has fixed costs of $3400 and a marginal cost of $3.86 per unit. Find the average cost function (i.e. the average cost per unit to produce x units). What is the horizontal asymptote of the graph of the average cost function? What information is provided by the horizontal asymptote?

(Essay)

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Question 108

Find the cubic or quartic function that models the data in the table. - 2 3 5 6 7 3 5 9 15 19 start text left parenthesisQuarticright parenthesis end text

(Multiple Choice)

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Question 109

Choose the graph that satisfies the given conditions. -Quartic polynomial with one x $x \text {-intercept }$ intercept and a positive leading coefficient

(Multiple Choice)

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Question 110

Solve the polynomial equation by using the root method. - $4 x ^ { 3 } - 108 = 0$

(Multiple Choice)

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Question 111

Match the polynomial function with the graph. - $y = x ^ { 4 } + 5$

(Multiple Choice)

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Question 112

$P ( x ) = - x ^ { 3 } + \frac { 27 } { 2 } x ^ { 2 } - 60 x + 100 , x \geq 5$ 5 is an approximation of the total profit (in thousands of dollars) from the sale of x hundred thousand tires. Find the number of hundred thousands of tires that must be sold to maximize Profit.

(Multiple Choice)

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Question 113

Solve the equation exactly in the complex number system. -The profit function for a product is given by $P ( x ) = - 0.3 x ^ { 3 } + 75 x ^ { 2 } - 2820 x - 36,000$ dollars, where x is the number of units produced and sold. If break-even occurs when 60 units are produced and sold, use synthetic division To find a quadratic factor of P(x) and then find a number of units other than 60 that gives break-even for the Product.

(Multiple Choice)

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Question 114

$f ( x ) = \frac { x ^ { 2 } + 3 x } { x - 1 }$ $f ( x ) = \frac { x ^ { 2 } + 3 x } { x - 1 }$

(Multiple Choice)

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Question 115

Match the polynomial function with the graph. - $y = - x ^ { 4 } + 9 x ^ { 2 }$

(Multiple Choice)

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Question 116

A population of birds in a small county can be modeled by the polynomial $f ( x ) = x ^ { 3 } - 57 x ^ { 2 } + 1162 x + 1094$ where x=1 corresponds to July 1, x=2 to July 2 , and so on. On what day does f estimate the population to be 8550 ?

(Multiple Choice)

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Question 117

Match the function with its graph. - $f ( x ) = \frac { x ^ { 2 } - 9 } { x + 2 }$

(Multiple Choice)

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Question 118

Use a graphing calculator to estimate the local maximum and local minimum values of the function to the nearest hundredth. -The following polynomial approximates the rabbit population in a particular area, R(x) = -0.135x5 + 2.952x4 + 3500, where x is the number of years from 1995. Use a graphing calculator to Describe the rabbit population from the years 1995 to 2010.

(Multiple Choice)

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Question 119

Determine whether the second polynomial is a factor of the first polynomial. - $\left( 5 x ^ { 3 } + 17 x ^ { 2 } - 11 x + 4 \right) ; ( x + 4 )$

(Multiple Choice)

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Question 120

Photon Lighting Company determines that the supply and demand functions for its most popular lamp are as follows: $S ( p ) = 300 - 3 p + 0.000015 p ^ { 4 } \text { and } D ( p ) = 2100 - 0.0009 p ^ { 3 }$ , where p is the price. Determine the price for which The supply equals the demand.

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - $- 3 x ^ { 4 } + 12 x ^ { 3 } + 3 x ^ { 2 } - 48 x + 36 = 0 ; 2$

Solve the polynomial equation. - $( 3 x + 1 ) ( x - 2 ) ^ { 2 } ( x + 6 ) = 0$

Determine all possible rational solutions of the polynomial equation. - $f ( x ) = 11 x ^ { 3 } + 19 x ^ { 2 } + 2 x - 22$

Find one solution graphically and then find the remaining solutions using synthetic division. - $x ^ { 3 } - 4 x ^ { 2 } - 36 x + 144 = 0$

$\frac { - 6 x + 2 } { 6 x ^ { 2 } + 6 } > 0$

The profit function for a product is given by $P ( x ) = - 0.7 x ^ { 3 } + 115.5 x ^ { 2 } - 3710 x - 84,000$ dollars, where x is the number of units produced and sold. Determine the levels of production and sale that give break-even.

A company has fixed costs of $3400 and a marginal cost of $3.86 per unit. Find the average cost function (i.e. the average cost per unit to produce x units). What is the horizontal asymptote of the graph of the average cost function? What information is provided by the horizontal asymptote?

Find the cubic or quartic function that models the data in the table. - 2 3 5 6 7 3 5 9 15 19 start text left parenthesisQuarticright parenthesis end text

Choose the graph that satisfies the given conditions. -Quartic polynomial with one x $x \text {-intercept }$ intercept and a positive leading coefficient

Solve the polynomial equation by using the root method. - $4 x ^ { 3 } - 108 = 0$

Match the polynomial function with the graph. - $y = x ^ { 4 } + 5$

$P ( x ) = - x ^ { 3 } + \frac { 27 } { 2 } x ^ { 2 } - 60 x + 100 , x \geq 5$ 5 is an approximation of the total profit (in thousands of dollars) from the sale of x hundred thousand tires. Find the number of hundred thousands of tires that must be sold to maximize Profit.

$f ( x ) = \frac { x ^ { 2 } + 3 x } { x - 1 }$ $f ( x ) = \frac { x ^ { 2 } + 3 x } { x - 1 }$

Match the polynomial function with the graph. - $y = - x ^ { 4 } + 9 x ^ { 2 }$

A population of birds in a small county can be modeled by the polynomial $f ( x ) = x ^ { 3 } - 57 x ^ { 2 } + 1162 x + 1094$ where x=1 corresponds to July 1, x=2 to July 2 , and so on. On what day does f estimate the population to be 8550 ?

Match the function with its graph. - $f ( x ) = \frac { x ^ { 2 } - 9 } { x + 2 }$

Determine whether the second polynomial is a factor of the first polynomial. - $\left( 5 x ^ { 3 } + 17 x ^ { 2 } - 11 x + 4 \right) ; ( x + 4 )$

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Exponential and Logarithmic Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

Exam 6: Higher-Degree Polynomial and Rational Functions

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - −3x4+12x3+3x2−48x+36=0;2- 3 x ^ { 4 } + 12 x ^ { 3 } + 3 x ^ { 2 } - 48 x + 36 = 0 ; 2−3x4+12x3+3x2−48x+36=0;2

Solve the polynomial equation. - (3x+1)(x−2)2(x+6)=0( 3 x + 1 ) ( x - 2 ) ^ { 2 } ( x + 6 ) = 0(3x+1)(x−2)2(x+6)=0

Determine all possible rational solutions of the polynomial equation. - f(x)=11x3+19x2+2x−22f ( x ) = 11 x ^ { 3 } + 19 x ^ { 2 } + 2 x - 22f(x)=11x3+19x2+2x−22

Find one solution graphically and then find the remaining solutions using synthetic division. - x3−4x2−36x+144=0x ^ { 3 } - 4 x ^ { 2 } - 36 x + 144 = 0x3−4x2−36x+144=0

−6x+26x2+6>0\frac { - 6 x + 2 } { 6 x ^ { 2 } + 6 } > 06x2+6−6x+2​>0

A company has fixed costs of $3400 and a marginal cost of $3.86 per unit. Find the average cost function (i.e. the average cost per unit to produce x units). What is the horizontal asymptote of the graph of the average cost function? What information is provided by the horizontal asymptote?

Find the cubic or quartic function that models the data in the table. - 2 3 5 6 7 3 5 9 15 19 start text left parenthesisQuarticright parenthesis end text

Choose the graph that satisfies the given conditions. -Quartic polynomial with one x x-intercept x \text {-intercept }x-intercept intercept and a positive leading coefficient

Solve the polynomial equation by using the root method. - 4x3−108=04 x ^ { 3 } - 108 = 04x3−108=0

Match the polynomial function with the graph. - y=x4+5y = x ^ { 4 } + 5y=x4+5

f(x)=x2+3xx−1f ( x ) = \frac { x ^ { 2 } + 3 x } { x - 1 }f(x)=x−1x2+3x​

Match the polynomial function with the graph. - y=−x4+9x2y = - x ^ { 4 } + 9 x ^ { 2 }y=−x4+9x2

A population of birds in a small county can be modeled by the polynomial f(x)=x3−57x2+1162x+1094f ( x ) = x ^ { 3 } - 57 x ^ { 2 } + 1162 x + 1094f(x)=x3−57x2+1162x+1094 where x=1 corresponds to July 1, x=2 to July 2 , and so on. On what day does f estimate the population to be 8550 ?

Match the function with its graph. - f(x)=x2−9x+2f ( x ) = \frac { x ^ { 2 } - 9 } { x + 2 }f(x)=x+2x2−9​

Determine whether the second polynomial is a factor of the first polynomial. - (5x3+17x2−11x+4);(x+4)\left( 5 x ^ { 3 } + 17 x ^ { 2 } - 11 x + 4 \right) ; ( x + 4 )(5x3+17x2−11x+4);(x+4)

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Exponential and Logarithmic Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - $- 3 x ^ { 4 } + 12 x ^ { 3 } + 3 x ^ { 2 } - 48 x + 36 = 0 ; 2$

Solve the polynomial equation. - $( 3 x + 1 ) ( x - 2 ) ^ { 2 } ( x + 6 ) = 0$

Determine all possible rational solutions of the polynomial equation. - $f ( x ) = 11 x ^ { 3 } + 19 x ^ { 2 } + 2 x - 22$

Find one solution graphically and then find the remaining solutions using synthetic division. - $x ^ { 3 } - 4 x ^ { 2 } - 36 x + 144 = 0$

$\frac { - 6 x + 2 } { 6 x ^ { 2 } + 6 } > 0$

Choose the graph that satisfies the given conditions. -Quartic polynomial with one x $x \text {-intercept }$ intercept and a positive leading coefficient

Solve the polynomial equation by using the root method. - $4 x ^ { 3 } - 108 = 0$

Match the polynomial function with the graph. - $y = x ^ { 4 } + 5$

$f ( x ) = \frac { x ^ { 2 } + 3 x } { x - 1 }$ $f ( x ) = \frac { x ^ { 2 } + 3 x } { x - 1 }$

Match the polynomial function with the graph. - $y = - x ^ { 4 } + 9 x ^ { 2 }$

A population of birds in a small county can be modeled by the polynomial $f ( x ) = x ^ { 3 } - 57 x ^ { 2 } + 1162 x + 1094$ where x=1 corresponds to July 1, x=2 to July 2 , and so on. On what day does f estimate the population to be 8550 ?

Match the function with its graph. - $f ( x ) = \frac { x ^ { 2 } - 9 } { x + 2 }$

Determine whether the second polynomial is a factor of the first polynomial. - $\left( 5 x ^ { 3 } + 17 x ^ { 2 } - 11 x + 4 \right) ; ( x + 4 )$