Question 1

Find the axis of symmetry of the quadratic function.
-$$f ( x ) = 11 ( x - 4 ) ^ { 2 } + 6$$

Accepted Answer

A)  $x = - 4$ 
B)  $x = 4$ 
C)  $x = 6$ 
D)  $x = 11$ 
A)  $x = - 4$ 
B)  $x = 4$ 
C)  $x = 6$ 
D)  $x = 11$ B

Question 2

Determine the real zeros of the polynomial and their multiplicities. Then decide whether the graph touches or crosses the
x-axis at each zero.

-$$f ( x ) = 5 ( x - 4 ) ( x - 6 ) ^ { 3 }$$

Accepted Answer

A) 4, multiplicity 1, crosses x-axis; 6, multiplicity 3, crosses x-axis 
B) -4, multiplicity 1, crosses x-axis; -6, multiplicity 3, crosses x-axis 
C) -4, multiplicity 1, touches x-axis; -6, multiplicity 3 
D) 4, multiplicity 1, touches x-axis; 6, multiplicity 3 
A) 4, multiplicity 1, crosses x-axis; 6, multiplicity 3, crosses x-axis 
B) -4, multiplicity 1, crosses x-axis; -6, multiplicity 3, crosses x-axis 
C) -4, multiplicity 1, touches x-axis; -6, multiplicity 3 
D) 4, multiplicity 1, touches x-axis; 6, multiplicity 3 A

Question 3

Solve the polynomial equation in the complex numbers.
-$x ^ { 4 } - 8 x ^ { 3 } + 22 x ^ { 2 } + 12 x - 144 = 0$

Accepted Answer

A)  $\{ - 2,4,3 + 4 i , 3 - 4 i \}$ 
B)  $\{ 2 , - 4,3 + \sqrt { 3 } , 3 - \sqrt { 3 } \}$ 
C)  $\{ 2 , - 4,3 + 3 i , 3 - 3 i \}$ 
D)  $\{ - 2,4,3 + 3 i , 3 - 3 i \}$ 
A)  $\{ - 2,4,3 + 4 i , 3 - 4 i \}$ 
B)  $\{ 2 , - 4,3 + \sqrt { 3 } , 3 - \sqrt { 3 } \}$ 
C)  $\{ 2 , - 4,3 + 3 i , 3 - 3 i \}$ 
D)  $\{ - 2,4,3 + 3 i , 3 - 3 i \}$ D

Question 4

Find the remaining zeros of f(x)given that c is a zero. Then rewrite f(x)in completely factored form.
-$f ( x ) = 3 x ^ { 3 } - 8 x ^ { 2 } - 5 x + 6 ; c = - 1$ is a zero

Accepted Answer

A)  $\frac { 3 } { 2 } , - 3 ; f ( x ) = ( 3 x - 2 ) ( x - 3 ) ( x + 1 )$ 
B)  $- 3,1 , \frac { 3 } { 2 } ; f ( x ) = ( 3 x - 2 ) ( x - 1 ) ( x + 3 )$ 
C)  $\frac { 2 } { 3 } , 3 ; f ( x ) = ( 3 x - 2 ) ( x - 3 ) ( x + 1 )$ 
D)  $- 3 , \frac { 2 } { 3 } , 1 ; f ( x ) = ( 3 x - 2 ) ( x - 1 ) ( x + 3 )$ 
A)  $\frac { 3 } { 2 } , - 3 ; f ( x ) = ( 3 x - 2 ) ( x - 3 ) ( x + 1 )$ 
B)  $- 3,1 , \frac { 3 } { 2 } ; f ( x ) = ( 3 x - 2 ) ( x - 1 ) ( x + 3 )$ 
C)  $\frac { 2 } { 3 } , 3 ; f ( x ) = ( 3 x - 2 ) ( x - 3 ) ( x + 1 )$ 
D)  $- 3 , \frac { 2 } { 3 } , 1 ; f ( x ) = ( 3 x - 2 ) ( x - 1 ) ( x + 3 )$

Question 5

Determine the possible number of positive real zeros and negative real zeros of the polynomial function using Descartes' rule of signs.
-$$f ( x ) = 7 x ^ { 3 } - 6 x ^ { 2 } + x + 3.5$$

Accepted Answer

A) 3 or 1 positive zeros, 1 negative zero 
B) 2 or 0 positive zeros, no negative zeros 
C) 2 or 0 positive zeros, 1 negative zero 
D) 3 or 1 positive zeros, 2 or 0 negative zeros 
A) 3 or 1 positive zeros, 1 negative zero 
B) 2 or 0 positive zeros, no negative zeros 
C) 2 or 0 positive zeros, 1 negative zero 
D) 3 or 1 positive zeros, 2 or 0 negative zeros

Question 6

Find the domain of the rational function.
-$$f ( x ) = \frac { - 3 x ^ { 2 } } { x ^ { 2 } + 9 x - 36 }$$

Accepted Answer

A)  $\{ x \mid x \neq - 36,1 \}$ 
B)  $\{ x \mid x \neq 12,3 \}$ 
C)  $\{ x \mid x \neq 12 , - 3 \}$ 
D)  $\{ x \mid x \neq - 12,3 \}$ 
A)  $\{ x \mid x \neq - 36,1 \}$ 
B)  $\{ x \mid x \neq 12,3 \}$ 
C)  $\{ x \mid x \neq 12 , - 3 \}$ 
D)  $\{ x \mid x \neq - 12,3 \}$

Question 7

Find the vertical asymptotes, if any, of the graph of the rational function.
-$$f ( x ) = \frac { 9 x ^ { 2 } - 5 x - 4 } { 3 x ^ { 2 } - 6 x + 7 }$$

Accepted Answer

A)  $y = \frac { 5 } { 6 }$ 
B)  $y = 0$ 
C)  $y = 3$ 
D)  none 
A)  $y = \frac { 5 } { 6 }$ 
B)  $y = 0$ 
C)  $y = 3$ 
D)  none

Question 8

Solve the problem.
-The manufacturer of a CD player has found that the revenue R (in dollars)is $$R ( p ) = - 5 p ^ { 2 } + 1590 p$$ when the unit price is p dollars. If the manufacturer sets the price p to maximize revenue, what is the maximum revenue to the nearest whole dollar?

Accepted Answer

A) $252,810 
B) $1,011,240 
C) $505,620 
D) $126,405 
A) $252,810 
B) $1,011,240 
C) $505,620 
D) $126,405

Question 9

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

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 10

Give the equation of the slant asymptote, if any, of the function.
-$$f ( x ) = \frac { x ^ { 2 } + 3 x + 9 } { x + 5 }$$

Accepted Answer

A) none 
B) x = y - 2 
C) y = x - 8 
D) y = x - 2 
A) none 
B) x = y - 2 
C) y = x - 8 
D) y = x - 2

Question 11

Graph the function.
-$f(x)=\frac{x^{2}}{x^{2}-x-72}$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 12

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value.
-$$f ( x ) = \frac { 1 } { 2 } x ^ { 2 } + 4 x - 4$$

Accepted Answer

A)  minimum at $( - 4 , - 12 )$ 
B)  maximum at $( 4,6 )$ 
C)  minimum at $( 4,12 )$ 
D)  maximum at $( - 4 , - 4 )$ 
A)  minimum at $( - 4 , - 12 )$ 
B)  maximum at $( 4,6 )$ 
C)  minimum at $( 4,12 )$ 
D)  maximum at $( - 4 , - 4 )$

Question 13

Use the graph of a power function and transformations to sketch the graph of the polynomial function.

-$$( x ) = 3 - ( x + 2 ) ^ { 4 }$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 14

Use the graph of a power function and transformations to sketch the graph of the polynomial function.

-$$f ( x ) = \frac { 1 } { 2 } ( x + 3 ) ^ { 4 } + 2$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 15

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

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 16

Find all complex zeros of the polynomial function, and write the polynomial in completely factored form.
-$$f ( x ) = 3 x ^ { 4 } + 4 x ^ { 3 } + 28 x ^ { 2 } + 36 x + 9$$

Accepted Answer

A)  $f ( x ) = ( 3 x - 1 ) ( x - 1 ) ( x + 3 i ) ( x - 3 i )$ 
B)  $f ( x ) = ( 3 x + 1 ) ( x + 1 ) ( x + 3 ) ( x - 3 )$ 
C)  $f ( x ) = ( 3 x + 1 ) ( x + 1 ) ( x + 3 i ) ( x - 3 i )$ 
D)  $f ( x ) = ( 3 x - 1 ) ( x - 1 ) ( x + 3 ) ( x - 3 )$ 
A)  $f ( x ) = ( 3 x - 1 ) ( x - 1 ) ( x + 3 i ) ( x - 3 i )$ 
B)  $f ( x ) = ( 3 x + 1 ) ( x + 1 ) ( x + 3 ) ( x - 3 )$ 
C)  $f ( x ) = ( 3 x + 1 ) ( x + 1 ) ( x + 3 i ) ( x - 3 i )$ 
D)  $f ( x ) = ( 3 x - 1 ) ( x - 1 ) ( x + 3 ) ( x - 3 )$

Question 17

Graph the polynomial function.
-

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 18

Use the graph of a power function and transformations to sketch the graph of the polynomial function.

-

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 19

Find all complex zeros of the polynomial function, and write the polynomial in completely factored form.
-$$f ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 33 x + 34$$

Accepted Answer

A)  $f ( x ) = ( x + 1 ) ( x + 4 + i \sqrt { 3 } ) ( x - 2 - i \sqrt { 3 } )$ 
B)  $f ( x ) = ( x + 2 ) ( x + 4 + i ) ( x + 4 - i )$ 
C)  $f ( x ) = ( x - 1 ) ( x + 4 + i \sqrt { 3 } ) ( x + 4 - i \sqrt { 3 } )$ 
D)  $f ( x ) = ( x + 2 ) ( x + 4 + i ) ( x - 4 - i )$ 
A)  $f ( x ) = ( x + 1 ) ( x + 4 + i \sqrt { 3 } ) ( x - 2 - i \sqrt { 3 } )$ 
B)  $f ( x ) = ( x + 2 ) ( x + 4 + i ) ( x + 4 - i )$ 
C)  $f ( x ) = ( x - 1 ) ( x + 4 + i \sqrt { 3 } ) ( x + 4 - i \sqrt { 3 } )$ 
D)  $f ( x ) = ( x + 2 ) ( x + 4 + i ) ( x - 4 - i )$

Question 20

Find the axis of symmetry of the quadratic function.
-$$f ( x ) = - 3 x ^ { 2 } - 6 x + 8$$

Accepted Answer

A)  $x = - 2$ 
B)  $x = - 1$ 
C)  $x = 1$ 
D)  $x = 11$ 
A)  $x = - 2$ 
B)  $x = - 1$ 
C)  $x = 1$ 
D)  $x = 11$

Find the axis of symmetry of the quadratic function. - $f ( x ) = 11 ( x - 4 ) ^ { 2 } + 6$

Determine the real zeros of the polynomial and their multiplicities. Then decide whether the graph touches or crosses the x-axis at each zero. - $f ( x ) = 5 ( x - 4 ) ( x - 6 ) ^ { 3 }$

Solve the polynomial equation in the complex numbers. - $x ^ { 4 } - 8 x ^ { 3 } + 22 x ^ { 2 } + 12 x - 144 = 0$

Find the remaining zeros of f(x)given that c is a zero. Then rewrite f(x)in completely factored form. - $f ( x ) = 3 x ^ { 3 } - 8 x ^ { 2 } - 5 x + 6 ; c = - 1$ is a zero

Determine the possible number of positive real zeros and negative real zeros of the polynomial function using Descartes' rule of signs. - $f ( x ) = 7 x ^ { 3 } - 6 x ^ { 2 } + x + 3.5$

Find the domain of the rational function. - $f ( x ) = \frac { - 3 x ^ { 2 } } { x ^ { 2 } + 9 x - 36 }$

Find the vertical asymptotes, if any, of the graph of the rational function. - $f ( x ) = \frac { 9 x ^ { 2 } - 5 x - 4 } { 3 x ^ { 2 } - 6 x + 7 }$

Solve the problem. -The manufacturer of a CD player has found that the revenue R (in dollars)is $R ( p ) = - 5 p ^ { 2 } + 1590 p$ when the unit price is p dollars. If the manufacturer sets the price p to maximize revenue, what is the maximum revenue to the nearest whole dollar?

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

Give the equation of the slant asymptote, if any, of the function. - $f ( x ) = \frac { x ^ { 2 } + 3 x + 9 } { x + 5 }$

Graph the function. - $f(x)=\frac{x^{2}}{x^{2}-x-72}$ $Graph the function. - f(x)=\frac{x^{2}}{x^{2}-x-72}$

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value. - $f ( x ) = \frac { 1 } { 2 } x ^ { 2 } + 4 x - 4$

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - $( x ) = 3 - ( x + 2 ) ^ { 4 }$ $Use the graph of a power function and transformations to sketch the graph of the polynomial function. - ( x ) = 3 - ( x + 2 ) ^ { 4 }$

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

Find all complex zeros of the polynomial function, and write the polynomial in completely factored form. - $f ( x ) = 3 x ^ { 4 } + 4 x ^ { 3 } + 28 x ^ { 2 } + 36 x + 9$

Graph the polynomial function. -

Use the graph of a power function and transformations to sketch the graph of the polynomial function. -

Find all complex zeros of the polynomial function, and write the polynomial in completely factored form. - $f ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 33 x + 34$

Find the axis of symmetry of the quadratic function. - $f ( x ) = - 3 x ^ { 2 } - 6 x + 8$

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Exam 4: Polynomial and Rational Functions

Find the axis of symmetry of the quadratic function. - f(x)=11(x−4)2+6f ( x ) = 11 ( x - 4 ) ^ { 2 } + 6f(x)=11(x−4)2+6

Determine the real zeros of the polynomial and their multiplicities. Then decide whether the graph touches or crosses the x-axis at each zero. - f(x)=5(x−4)(x−6)3f ( x ) = 5 ( x - 4 ) ( x - 6 ) ^ { 3 }f(x)=5(x−4)(x−6)3

Solve the polynomial equation in the complex numbers. - x4−8x3+22x2+12x−144=0x ^ { 4 } - 8 x ^ { 3 } + 22 x ^ { 2 } + 12 x - 144 = 0x4−8x3+22x2+12x−144=0

Find the remaining zeros of f(x)given that c is a zero. Then rewrite f(x)in completely factored form. - f(x)=3x3−8x2−5x+6;c=−1f ( x ) = 3 x ^ { 3 } - 8 x ^ { 2 } - 5 x + 6 ; c = - 1f(x)=3x3−8x2−5x+6;c=−1 is a zero

Determine the possible number of positive real zeros and negative real zeros of the polynomial function using Descartes' rule of signs. - f(x)=7x3−6x2+x+3.5f ( x ) = 7 x ^ { 3 } - 6 x ^ { 2 } + x + 3.5f(x)=7x3−6x2+x+3.5

Find the domain of the rational function. - f(x)=−3x2x2+9x−36f ( x ) = \frac { - 3 x ^ { 2 } } { x ^ { 2 } + 9 x - 36 }f(x)=x2+9x−36−3x2​

Find the vertical asymptotes, if any, of the graph of the rational function. - f(x)=9x2−5x−43x2−6x+7f ( x ) = \frac { 9 x ^ { 2 } - 5 x - 4 } { 3 x ^ { 2 } - 6 x + 7 }f(x)=3x2−6x+79x2−5x−4​

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

Give the equation of the slant asymptote, if any, of the function. - f(x)=x2+3x+9x+5f ( x ) = \frac { x ^ { 2 } + 3 x + 9 } { x + 5 }f(x)=x+5x2+3x+9​

Graph the function. - f(x)=x2x2−x−72f(x)=\frac{x^{2}}{x^{2}-x-72}f(x)=x2−x−72x2​

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value. - f(x)=12x2+4x−4f ( x ) = \frac { 1 } { 2 } x ^ { 2 } + 4 x - 4f(x)=21​x2+4x−4

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - (x)=3−(x+2)4( x ) = 3 - ( x + 2 ) ^ { 4 }(x)=3−(x+2)4

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f(x)=12(x+3)4+2f ( x ) = \frac { 1 } { 2 } ( x + 3 ) ^ { 4 } + 2f(x)=21​(x+3)4+2

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

Find all complex zeros of the polynomial function, and write the polynomial in completely factored form. - f(x)=3x4+4x3+28x2+36x+9f ( x ) = 3 x ^ { 4 } + 4 x ^ { 3 } + 28 x ^ { 2 } + 36 x + 9f(x)=3x4+4x3+28x2+36x+9

Graph the polynomial function. -

Use the graph of a power function and transformations to sketch the graph of the polynomial function. -

Find all complex zeros of the polynomial function, and write the polynomial in completely factored form. - f(x)=x3+10x2+33x+34f ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 33 x + 34f(x)=x3+10x2+33x+34

Find the axis of symmetry of the quadratic function. - f(x)=−3x2−6x+8f ( x ) = - 3 x ^ { 2 } - 6 x + 8f(x)=−3x2−6x+8

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Find the axis of symmetry of the quadratic function. - $f ( x ) = 11 ( x - 4 ) ^ { 2 } + 6$

Determine the real zeros of the polynomial and their multiplicities. Then decide whether the graph touches or crosses the x-axis at each zero. - $f ( x ) = 5 ( x - 4 ) ( x - 6 ) ^ { 3 }$

Solve the polynomial equation in the complex numbers. - $x ^ { 4 } - 8 x ^ { 3 } + 22 x ^ { 2 } + 12 x - 144 = 0$

Find the remaining zeros of f(x)given that c is a zero. Then rewrite f(x)in completely factored form. - $f ( x ) = 3 x ^ { 3 } - 8 x ^ { 2 } - 5 x + 6 ; c = - 1$ is a zero

Determine the possible number of positive real zeros and negative real zeros of the polynomial function using Descartes' rule of signs. - $f ( x ) = 7 x ^ { 3 } - 6 x ^ { 2 } + x + 3.5$

Find the domain of the rational function. - $f ( x ) = \frac { - 3 x ^ { 2 } } { x ^ { 2 } + 9 x - 36 }$

Find the vertical asymptotes, if any, of the graph of the rational function. - $f ( x ) = \frac { 9 x ^ { 2 } - 5 x - 4 } { 3 x ^ { 2 } - 6 x + 7 }$

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

Give the equation of the slant asymptote, if any, of the function. - $f ( x ) = \frac { x ^ { 2 } + 3 x + 9 } { x + 5 }$

Graph the function. - $f(x)=\frac{x^{2}}{x^{2}-x-72}$ $Graph the function. - f(x)=\frac{x^{2}}{x^{2}-x-72}$

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value. - $f ( x ) = \frac { 1 } { 2 } x ^ { 2 } + 4 x - 4$

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - $( x ) = 3 - ( x + 2 ) ^ { 4 }$ $Use the graph of a power function and transformations to sketch the graph of the polynomial function. - ( x ) = 3 - ( x + 2 ) ^ { 4 }$

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

Find all complex zeros of the polynomial function, and write the polynomial in completely factored form. - $f ( x ) = 3 x ^ { 4 } + 4 x ^ { 3 } + 28 x ^ { 2 } + 36 x + 9$

Find all complex zeros of the polynomial function, and write the polynomial in completely factored form. - $f ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 33 x + 34$

Find the axis of symmetry of the quadratic function. - $f ( x ) = - 3 x ^ { 2 } - 6 x + 8$