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Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function. - P(x) =4x43x37x24x+7P ( x ) = - 4 x ^ { 4 } - 3 x ^ { 3 } - 7 x ^ { 2 } - 4 x + 7


A) 0 or 2 positive; 1 or 3 negative
B) 1 positive; 2 negative
C) 1 positive; 1 or 3 negative
D) 1 positive; 1 negative

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Solve. -The profit made when tt units are sold is given by P=t224t+140P = t ^ { 2 } - 24 t + 140 for t>0t > 0 . Determine the values of tt for which P<0P < 0 (a loss is taken) .


A) (10,14) ( 10,14 )
B) (0,) ( 0 , \infty )
C) [10,14][ 10,14 ]
D) (,10) (14,) ( - \infty , 10 ) \cup ( 14 , \infty )

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Solve. - x2+10x+250x ^ { 2 } + 10 x + 25 \leq 0


A) [5,) [ 5 , \infty )
B) {5}\{ 5 \}
C) (,5][5,) ( - \infty , - 5 ] \cup [ - 5 , \infty )
D) {5}\{ - 5 \}

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Find the horizontal asymptote, if any, of the rational function. - f(x) =3x39x77x35x+2f ( x ) = \frac { 3 x ^ { 3 } - 9 x - 7 } { 7 x ^ { 3 } - 5 x + 2 }


A) y=37y = \frac { 3 } { 7 }
B) y=95y = \frac { 9 } { 5 }
C) y=0\mathrm { y } = 0
D) None

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A

Graph the function, showing all asymptotes (those that do not correspond to an axis) as dashed lines. List the x- and y-intercepts. - f(x) =x23x43x2+2f ( x ) = \frac { x ^ { 2 } - 3 x - 4 } { 3 x ^ { 2 } + 2 }  Graph the function, showing all asymptotes (those that do not correspond to an axis)  as dashed lines. List the x- and y-intercepts. - f ( x )  = \frac { x ^ { 2 } - 3 x - 4 } { 3 x ^ { 2 } + 2 }    A)  No  x -intercepts,  y -intercept:  ( 0 , - 4 )  ;   B)  No  x -intercepts,  y -intercept:  ( 0 , - 4 )  ;   C)  x-intercepts:  ( 1,0 )   and  ( - 4,0 )  ,   D)  x-intercepts:  ( - 1,0 )   and  ( 4,0 )  , y-intercept:  ( 0 , - 2 )  ;  \mathrm { y } -intercept:  ( 0 , - 2 )  ;


A) No xx -intercepts, yy -intercept: (0,4) ( 0 , - 4 ) ;
 Graph the function, showing all asymptotes (those that do not correspond to an axis)  as dashed lines. List the x- and y-intercepts. - f ( x )  = \frac { x ^ { 2 } - 3 x - 4 } { 3 x ^ { 2 } + 2 }    A)  No  x -intercepts,  y -intercept:  ( 0 , - 4 )  ;   B)  No  x -intercepts,  y -intercept:  ( 0 , - 4 )  ;   C)  x-intercepts:  ( 1,0 )   and  ( - 4,0 )  ,   D)  x-intercepts:  ( - 1,0 )   and  ( 4,0 )  , y-intercept:  ( 0 , - 2 )  ;  \mathrm { y } -intercept:  ( 0 , - 2 )  ;
B) No xx -intercepts, yy -intercept: (0,4) ( 0 , - 4 ) ;
 Graph the function, showing all asymptotes (those that do not correspond to an axis)  as dashed lines. List the x- and y-intercepts. - f ( x )  = \frac { x ^ { 2 } - 3 x - 4 } { 3 x ^ { 2 } + 2 }    A)  No  x -intercepts,  y -intercept:  ( 0 , - 4 )  ;   B)  No  x -intercepts,  y -intercept:  ( 0 , - 4 )  ;   C)  x-intercepts:  ( 1,0 )   and  ( - 4,0 )  ,   D)  x-intercepts:  ( - 1,0 )   and  ( 4,0 )  , y-intercept:  ( 0 , - 2 )  ;  \mathrm { y } -intercept:  ( 0 , - 2 )  ;
C) x-intercepts: (1,0) ( 1,0 ) and (4,0) ( - 4,0 ) ,
 Graph the function, showing all asymptotes (those that do not correspond to an axis)  as dashed lines. List the x- and y-intercepts. - f ( x )  = \frac { x ^ { 2 } - 3 x - 4 } { 3 x ^ { 2 } + 2 }    A)  No  x -intercepts,  y -intercept:  ( 0 , - 4 )  ;   B)  No  x -intercepts,  y -intercept:  ( 0 , - 4 )  ;   C)  x-intercepts:  ( 1,0 )   and  ( - 4,0 )  ,   D)  x-intercepts:  ( - 1,0 )   and  ( 4,0 )  , y-intercept:  ( 0 , - 2 )  ;  \mathrm { y } -intercept:  ( 0 , - 2 )  ;
D) x-intercepts: (1,0) ( - 1,0 ) and (4,0) ( 4,0 ) , y-intercept: (0,2) ( 0 , - 2 ) ; y\mathrm { y } -intercept: (0,2) ( 0 , - 2 ) ;
 Graph the function, showing all asymptotes (those that do not correspond to an axis)  as dashed lines. List the x- and y-intercepts. - f ( x )  = \frac { x ^ { 2 } - 3 x - 4 } { 3 x ^ { 2 } + 2 }    A)  No  x -intercepts,  y -intercept:  ( 0 , - 4 )  ;   B)  No  x -intercepts,  y -intercept:  ( 0 , - 4 )  ;   C)  x-intercepts:  ( 1,0 )   and  ( - 4,0 )  ,   D)  x-intercepts:  ( - 1,0 )   and  ( 4,0 )  , y-intercept:  ( 0 , - 2 )  ;  \mathrm { y } -intercept:  ( 0 , - 2 )  ;

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Sketch the graph of the polynomial function. Use the rational zeros theorem when finding the zeros. - f(x) =2x3+x213x+6f ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 13 x + 6  Sketch the graph of the polynomial function. Use the rational zeros theorem when finding the zeros. - f ( x )  = 2 x ^ { 3 } + x ^ { 2 } - 13 x + 6    A)    B)    C)    D)


A)
 Sketch the graph of the polynomial function. Use the rational zeros theorem when finding the zeros. - f ( x )  = 2 x ^ { 3 } + x ^ { 2 } - 13 x + 6    A)    B)    C)    D)
B)
 Sketch the graph of the polynomial function. Use the rational zeros theorem when finding the zeros. - f ( x )  = 2 x ^ { 3 } + x ^ { 2 } - 13 x + 6    A)    B)    C)    D)
C)
 Sketch the graph of the polynomial function. Use the rational zeros theorem when finding the zeros. - f ( x )  = 2 x ^ { 3 } + x ^ { 2 } - 13 x + 6    A)    B)    C)    D)
D)
 Sketch the graph of the polynomial function. Use the rational zeros theorem when finding the zeros. - f ( x )  = 2 x ^ { 3 } + x ^ { 2 } - 13 x + 6    A)    B)    C)    D)

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Find only the rational zeros. - f(x) =x48x3+4x2+24x21f ( x ) = x ^ { 4 } - 8 x ^ { 3 } + 4 x ^ { 2 } + 24 x - 21


A) 7,1- 7,1
B) 7,1
C) 7,17 , - 1
D) No rational zeros

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Find the requested polynomial. -Find a polynomial function of degree 3 with 4,0,12- 4,0 , \frac { 1 } { 2 } as zeros.


A) f(x) =x372x2+2xf ( x ) = x ^ { 3 } - \frac { 7 } { 2 } x ^ { 2 } + 2 x
B) f(x) =x3+92x22xf ( x ) = x ^ { 3 } + \frac { 9 } { 2 } x ^ { 2 } - 2 x
C) f(x) =x372x22xf ( x ) = x ^ { 3 } - \frac { 7 } { 2 } x ^ { 2 } - 2 x
D) f(x) =x3+72x22xf ( x ) = x ^ { 3 } + \frac { 7 } { 2 } x ^ { 2 } - 2 x

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Use the leading-term test to match the function with the correct graph. - f(x) =x5x3+x2+4f ( x ) = x ^ { 5 } - x ^ { 3 } + x ^ { 2 } + 4


A)
 Use the leading-term test to match the function with the correct graph. - f ( x )  = x ^ { 5 } - x ^ { 3 } + x ^ { 2 } + 4  A)    B)    C)    D)
B)
 Use the leading-term test to match the function with the correct graph. - f ( x )  = x ^ { 5 } - x ^ { 3 } + x ^ { 2 } + 4  A)    B)    C)    D)
C)
 Use the leading-term test to match the function with the correct graph. - f ( x )  = x ^ { 5 } - x ^ { 3 } + x ^ { 2 } + 4  A)    B)    C)    D)
D)
 Use the leading-term test to match the function with the correct graph. - f ( x )  = x ^ { 5 } - x ^ { 3 } + x ^ { 2 } + 4  A)    B)    C)    D)

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Use the leading-term test to match the function with the correct graph. - f(x) =0.3x7+0.14x60.13x5+x4+x38x5f ( x ) = - 0.3 x ^ { 7 } + 0.14 x ^ { 6 } - 0.13 x ^ { 5 } + x ^ { 4 } + x ^ { 3 } - 8 x - 5


A)
 Use the leading-term test to match the function with the correct graph. - f ( x )  = - 0.3 x ^ { 7 } + 0.14 x ^ { 6 } - 0.13 x ^ { 5 } + x ^ { 4 } + x ^ { 3 } - 8 x - 5  A)    B)    C)    D)
B)
 Use the leading-term test to match the function with the correct graph. - f ( x )  = - 0.3 x ^ { 7 } + 0.14 x ^ { 6 } - 0.13 x ^ { 5 } + x ^ { 4 } + x ^ { 3 } - 8 x - 5  A)    B)    C)    D)
C)
 Use the leading-term test to match the function with the correct graph. - f ( x )  = - 0.3 x ^ { 7 } + 0.14 x ^ { 6 } - 0.13 x ^ { 5 } + x ^ { 4 } + x ^ { 3 } - 8 x - 5  A)    B)    C)    D)
D)
 Use the leading-term test to match the function with the correct graph. - f ( x )  = - 0.3 x ^ { 7 } + 0.14 x ^ { 6 } - 0.13 x ^ { 5 } + x ^ { 4 } + x ^ { 3 } - 8 x - 5  A)    B)    C)    D)

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D

Provide the requested response. -Suppose that a polynomial function of degree 4 with rational coefficients has 6, 4, 3i as zeros. Find the other zero.


A) 3- i
B) - 3i
C) -6  D)  3i\text { D) } \sqrt { 3 } \mathrm { i }

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Use long division to determine whether the binomial is a factor of f(x) . - f(x) =x4x33x2+4x+7;x+2f ( x ) = x ^ { 4 } - x ^ { 3 } - 3 x ^ { 2 } + 4 x + 7 ; x + 2


A) Yes
B) No\mathrm { No }

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Solve the inequality. -For the function h(x) =2x(x2) (x6) h ( x ) = \frac { 2 x } { ( x - 2 ) ( x - 6 ) } , solve h(x) <0h ( x ) < 0 .


A) (,2) (6,) ( - \infty , 2 ) \cup ( 6 , \infty )
B) (,0) (2,6) ( - \infty , 0 ) \cup ( 2,6 )
C) [2,6][ 2,6 ]
D) (,2][6,) ( - \infty , 2 ] \cup [ 6 , \infty )

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Solve. - x3+5x24x200x ^ { 3 } + 5 x ^ { 2 } - 4 x - 20 \geq 0


A) [5,) [ - 5 , \infty )
B) [5,2][2,) [ - 5 , - 2 ] \cup [ 2 , \infty )
C) [2,2][5,) [ - 2,2 ] \cup [ 5 , \infty )
D) [5,2][ - 5,2 ]

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Find the vertical asymptote(s) of the graph of the given function. - g(x) =x+7x3g ( x ) = \frac { x + 7 } { x - 3 }


A) x=7x = - 7
B) x=3x = 3
C) x=3x = - 3
D) y=3y = 3

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B

Solve the inequality. -For the function f(x) =x22x35f ( x ) = x ^ { 2 } - 2 x - 35 , solve f(x) 0f ( x ) \leq 0 .


A) (,5][7,) ( - \infty , - 5 ] \cup [ 7 , \infty )
B) [5,7][ - 5,7 ]
C) (,5]( - \infty , - 5 ]
D) [7,) [ 7 , \infty )

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Provide the requested response. -Suppose that a polynomial function of degree 5 with rational coefficients has 5,4,3,5i- 5,4 , - 3,5 - i as zeros. Find the other zero(s) .


A) 5+i5 + i
B) 5i- 5 - \mathrm { i }
C) 5,4,3,5+i5 , - 4,3,5 + \mathrm { i }
D) 5+i- 5 + \mathrm { i }

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Graph the function. - f(x) =x33x2f ( x ) = x ^ { 3 } - 3 x ^ { 2 }  Graph the function. - f ( x )  = x ^ { 3 } - 3 x ^ { 2 }    A)    B)    C)    D)


A)
 Graph the function. - f ( x )  = x ^ { 3 } - 3 x ^ { 2 }    A)    B)    C)    D)
B)
 Graph the function. - f ( x )  = x ^ { 3 } - 3 x ^ { 2 }    A)    B)    C)    D)
C)
 Graph the function. - f ( x )  = x ^ { 3 } - 3 x ^ { 2 }    A)    B)    C)    D)
D)
 Graph the function. - f ( x )  = x ^ { 3 } - 3 x ^ { 2 }    A)    B)    C)    D)

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Find the correct end behavior diagram for the given polynomial function. - f(x)=x6+3x5x24x+3f ( x ) = - x ^ { 6 } + 3 x ^ { 5 } - x ^ { 2 } - 4 x + 3  Find the correct end behavior diagram for the given polynomial function. - f ( x ) = - x ^ { 6 } + 3 x ^ { 5 } - x ^ { 2 } - 4 x + 3

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Use synthetic division to find the quotient and the remainder. - (3x4+2x21) ÷(x+12) \left( 3 x ^ { 4 } + 2 x ^ { 2 } - 1 \right) \div \left( x + \frac { 1 } { 2 } \right)


A) Q(x) =3x3+32x2118x+118;R(x) =516Q ( x ) = 3 x ^ { 3 } + \frac { 3 } { 2 } x ^ { 2 } - \frac { 11 } { 8 } x + \frac { 11 } { 8 } ; R ( x ) = - \frac { 5 } { 16 }
B) Q(x) =3x31;R(x) =2Q ( x ) = 3 x ^ { 3 } - 1 ; R ( x ) = - 2
C) Q(x) =3x31;R(x) =0Q ( x ) = 3 x ^ { 3 } - 1 ; R ( x ) = 0
D) Q(x) =3x332x2+114x118;R(x) =516Q ( x ) = 3 x ^ { 3 } - \frac { 3 } { 2 } x ^ { 2 } + \frac { 11 } { 4 } x - \frac { 11 } { 8 } ; R ( x ) = - \frac { 5 } { 16 }

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