Find the cubic or quartic function that models the data in the table. -$\begin{array}{c|cccc} x & 3 & 4 & 6 & 8 \\ \hline y & 10 & 15 & 21 & 33 \end{array} \text { (Cubic) }$

A) $y = 0.28 x ^ { 3 } - 5.35 x ^ { 2 } + 22.97 x - 33.40$ B) $y = 0.38 x ^ { 3 } - 4.35 x ^ { 2 } + 22.97 x - 33.40$ C) $y = 0.38 x ^ { 3 } - 5.35 x ^ { 2 } + 24.97 x - 33.40$ D) $y = 0.28 x ^ { 3 } - 4.35 x ^ { 2 } + 24.97 x - 33.40$ A) $y = 0.28 x ^ { 3 } - 5.35 x ^ { 2 } + 22.97 x - 33.40$ B) $y = 0.38 x ^ { 3 } - 4.35 x ^ { 2 } + 22.97 x - 33.40$ C) $y = 0.38 x ^ { 3 } - 5.35 x ^ { 2 } + 24.97 x - 33.40$ D) $y = 0.28 x ^ { 3 } - 4.35 x ^ { 2 } + 24.97 x - 33.40$

Exam 6: Higher-Degree Polynomial and Rational Functions

Suppose c(x) $c ( x ) = x ^ { 3 } - 16 x ^ { 2 } + 20,000 x$ x is the cost of manufacturing x items. Find a production level that will minimize the average cost of making x items.

(Multiple Choice)

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Question 41

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 -$

(Multiple Choice)

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Question 42

Use the graph of f(x) to solve the inequality. - $f(x)<0$

(Multiple Choice)

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Question 43

$g ( x ) = \frac { x + 7 } { x ^ { 2 } - 6 }$

(Multiple Choice)

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Question 44

Find the cubic or quartic function that models the data in the table. - x 3 4 6 8 y 10 15 21 33 start text left parenthesisCubicright parenthesis end text

(Multiple Choice)

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Question 45

The Cool Company determines that the supply function for its basic air conditioning unit is $S ( p ) = 50 + 0.01 p ^ { 3 }$ and that its demand function is $D ( p ) = 250 - 0.2 p ^ { 2 }$ , where $p$ is the price. Determine the price for which the supply equals the demand.

(Multiple Choice)

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Question 46

Graph the function. - $f ( x ) = \frac { 2 x ^ { 2 } + 1 } { x - 1 }$ $Graph the function. - f ( x ) = \frac { 2 x ^ { 2 } + 1 } { x - 1 }$

(Multiple Choice)

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Question 47

$\frac { - 2 } { - 3 x - 2 } > 0$

(Multiple Choice)

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Question 48

State the degree and leading coefficient of the polynomial function. - $f ( x ) = - 13 x ^ { 4 } - 6 x ^ { 3 } - 7 x ^ { 2 } + 9$

(Multiple Choice)

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Question 49

Solve the polynomial equation by factoring. - $x ^ { 3 } - 6 x ^ { 2 } - x + 6 = 0$

(Multiple Choice)

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Question 50

Determine whether the given constant is a solution to the given polynomial equation. - $x ^ { 4 } + 7 x ^ { 2 } - 144 = 0 ; - 3$

(Multiple Choice)

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Question 51

Give the equations of any vertical asymptotes for the graphs of the rational functions. - $f ( x ) = \frac { x - 9 } { x ^ { 2 } + 7 x }$

(Multiple Choice)

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Question 52

Use the graph of f(x) to solve the inequality. -The profit made when $t$ units are sold, $t > 0$ , is given by $P = t ^ { 2 } - 34 t + 285$ . Determine the number of units to be sold in order for $\mathrm { P } > 0$ (a profit is made).

(Multiple Choice)

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Question 53

Graph the function. - $f ( x ) = \frac { 3x +1 } { x }$

(Multiple Choice)

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Question 54

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 -$

(Multiple Choice)

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Question 55

(Multiple Choice)

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Question 56

The table shows the number of dollars spent in Country X (in millions) on environmental protection programs during the years 2000(x=1) through 2010(x=11) . Find the cubic model that is the best fit for this data. Round coefficients to three decimal places. Year Spending (millions of dollars) 2000 5.5 2001 5.8 2002 6.1 2003 6.9 2004 7.1 2005 7.0 2006 6.5 2007 7.3 2008 7.6 2009 7.8 2010 7.9

(Multiple Choice)

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Question 57

Use factoring and the root method to solve the polynomial equation. - $11 x ^ { 4 } - 33 x ^ { 2 } = 0$

(Multiple Choice)

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Question 58

Predict the end behavior of the graph of the function. - $f ( x ) = - 1.25 x ^ { 4 } - x ^ { 3 } + x ^ { 2 } - 2 x + 3$

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Question 59

Use analytical methods to solve the equation. - $1 + \frac { 1 } { x } = \frac { 30 } { x ^ { 2 } }$

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Question 60

Suppose c(x) $c ( x ) = x ^ { 3 } - 16 x ^ { 2 } + 20,000 x$ x is the cost of manufacturing x items. Find a production level that will minimize the average cost of making x items.

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 -$

Use the graph of f(x) to solve the inequality. - $f(x)<0$

$g ( x ) = \frac { x + 7 } { x ^ { 2 } - 6 }$

Find the cubic or quartic function that models the data in the table. - x 3 4 6 8 y 10 15 21 33 start text left parenthesisCubicright parenthesis end text

The Cool Company determines that the supply function for its basic air conditioning unit is $S ( p ) = 50 + 0.01 p ^ { 3 }$ and that its demand function is $D ( p ) = 250 - 0.2 p ^ { 2 }$ , where $p$ is the price. Determine the price for which the supply equals the demand.

Graph the function. - $f ( x ) = \frac { 2 x ^ { 2 } + 1 } { x - 1 }$ $Graph the function. - f ( x ) = \frac { 2 x ^ { 2 } + 1 } { x - 1 }$

$\frac { - 2 } { - 3 x - 2 } > 0$

State the degree and leading coefficient of the polynomial function. - $f ( x ) = - 13 x ^ { 4 } - 6 x ^ { 3 } - 7 x ^ { 2 } + 9$

Solve the polynomial equation by factoring. - $x ^ { 3 } - 6 x ^ { 2 } - x + 6 = 0$

Determine whether the given constant is a solution to the given polynomial equation. - $x ^ { 4 } + 7 x ^ { 2 } - 144 = 0 ; - 3$

Give the equations of any vertical asymptotes for the graphs of the rational functions. - $f ( x ) = \frac { x - 9 } { x ^ { 2 } + 7 x }$

Use the graph of f(x) to solve the inequality. -The profit made when $t$ units are sold, $t > 0$ , is given by $P = t ^ { 2 } - 34 t + 285$ . Determine the number of units to be sold in order for $\mathrm { P } > 0$ (a profit is made).

Graph the function. - $f ( x ) = \frac { 3x +1 } { x }$

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 -$

Use factoring and the root method to solve the polynomial equation. - $11 x ^ { 4 } - 33 x ^ { 2 } = 0$

Predict the end behavior of the graph of the function. - $f ( x ) = - 1.25 x ^ { 4 } - x ^ { 3 } + x ^ { 2 } - 2 x + 3$

Use analytical methods to solve the equation. - $1 + \frac { 1 } { x } = \frac { 30 } { x ^ { 2 } }$

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

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Exam 6: Higher-Degree Polynomial and Rational Functions

Suppose c(x) c(x)=x3−16x2+20,000xc ( x ) = x ^ { 3 } - 16 x ^ { 2 } + 20,000 xc(x)=x3−16x2+20,000x x is the cost of manufacturing x items. Find a production level that will minimize the average cost of making x items.

Use the graph of the polynomial function f(x) to solve f( f(x) to solve f(x)=0f ( x ) \text { to solve } f ( x ) = 0f(x) to solve f(x)=0 -

Use the graph of f(x) to solve the inequality. - f(x)<0f(x)<0f(x)<0

g(x)=x+7x2−6g ( x ) = \frac { x + 7 } { x ^ { 2 } - 6 }g(x)=x2−6x+7​

Find the cubic or quartic function that models the data in the table. - x 3 4 6 8 y 10 15 21 33 start text left parenthesisCubicright parenthesis end text

Graph the function. - f(x)=2x2+1x−1f ( x ) = \frac { 2 x ^ { 2 } + 1 } { x - 1 }f(x)=x−12x2+1​

−2−3x−2>0\frac { - 2 } { - 3 x - 2 } > 0−3x−2−2​>0

State the degree and leading coefficient of the polynomial function. - f(x)=−13x4−6x3−7x2+9f ( x ) = - 13 x ^ { 4 } - 6 x ^ { 3 } - 7 x ^ { 2 } + 9f(x)=−13x4−6x3−7x2+9

Solve the polynomial equation by factoring. - x3−6x2−x+6=0x ^ { 3 } - 6 x ^ { 2 } - x + 6 = 0x3−6x2−x+6=0

Determine whether the given constant is a solution to the given polynomial equation. - x4+7x2−144=0;−3x ^ { 4 } + 7 x ^ { 2 } - 144 = 0 ; - 3x4+7x2−144=0;−3

Give the equations of any vertical asymptotes for the graphs of the rational functions. - f(x)=x−9x2+7xf ( x ) = \frac { x - 9 } { x ^ { 2 } + 7 x }f(x)=x2+7xx−9​

Use the graph of f(x) to solve the inequality. -The profit made when ttt units are sold, t>0t > 0t>0 , is given by P=t2−34t+285P = t ^ { 2 } - 34 t + 285P=t2−34t+285 . Determine the number of units to be sold in order for P>0\mathrm { P } > 0P>0 (a profit is made).

Graph the function. - f(x)=3x+1xf ( x ) = \frac { 3x +1 } { x }f(x)=x3x+1​

Use the graph of the polynomial function f(x) to solve f( f(x) to solve f(x)=0f ( x ) \text { to solve } f ( x ) = 0f(x) to solve f(x)=0 -

Use factoring and the root method to solve the polynomial equation. - 11x4−33x2=011 x ^ { 4 } - 33 x ^ { 2 } = 011x4−33x2=0

Predict the end behavior of the graph of the function. - f(x)=−1.25x4−x3+x2−2x+3f ( x ) = - 1.25 x ^ { 4 } - x ^ { 3 } + x ^ { 2 } - 2 x + 3f(x)=−1.25x4−x3+x2−2x+3

Use analytical methods to solve the equation. - 1+1x=30x21 + \frac { 1 } { x } = \frac { 30 } { x ^ { 2 } }1+x1​=x230​

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

Suppose c(x) $c ( x ) = x ^ { 3 } - 16 x ^ { 2 } + 20,000 x$ x is the cost of manufacturing x items. Find a production level that will minimize the average cost of making x items.

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 -$

Use the graph of f(x) to solve the inequality. - $f(x)<0$

$g ( x ) = \frac { x + 7 } { x ^ { 2 } - 6 }$

Graph the function. - $f ( x ) = \frac { 2 x ^ { 2 } + 1 } { x - 1 }$ $Graph the function. - f ( x ) = \frac { 2 x ^ { 2 } + 1 } { x - 1 }$

$\frac { - 2 } { - 3 x - 2 } > 0$

State the degree and leading coefficient of the polynomial function. - $f ( x ) = - 13 x ^ { 4 } - 6 x ^ { 3 } - 7 x ^ { 2 } + 9$

Solve the polynomial equation by factoring. - $x ^ { 3 } - 6 x ^ { 2 } - x + 6 = 0$

Determine whether the given constant is a solution to the given polynomial equation. - $x ^ { 4 } + 7 x ^ { 2 } - 144 = 0 ; - 3$

Give the equations of any vertical asymptotes for the graphs of the rational functions. - $f ( x ) = \frac { x - 9 } { x ^ { 2 } + 7 x }$

Use the graph of f(x) to solve the inequality. -The profit made when $t$ units are sold, $t > 0$ , is given by $P = t ^ { 2 } - 34 t + 285$ . Determine the number of units to be sold in order for $\mathrm { P } > 0$ (a profit is made).

Graph the function. - $f ( x ) = \frac { 3x +1 } { x }$

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 -$

Use factoring and the root method to solve the polynomial equation. - $11 x ^ { 4 } - 33 x ^ { 2 } = 0$

Predict the end behavior of the graph of the function. - $f ( x ) = - 1.25 x ^ { 4 } - x ^ { 3 } + x ^ { 2 } - 2 x + 3$

Use analytical methods to solve the equation. - $1 + \frac { 1 } { x } = \frac { 30 } { x ^ { 2 } }$