Question 1

Select the graph of the function $y = ( x / 3 ) ^ { 2 } - 5$ . Compare the graph of this function with the graph of $y = x ^ { 2 }$

Accepted Answer

A) 
 
Horizontal stretch and vertical shift. 
B) 
 
Horizontal stretch and vertical shift. 
C) 
 
Horizontal stretch and vertical shift. 
D) 
 
Horizontal stretch and vertical shift. 
E)

Horizontal stretch and vertical shift. 
A) 
 
Horizontal stretch and vertical shift. 
B) 
 
Horizontal stretch and vertical shift. 
C) 
 
Horizontal stretch and vertical shift. 
D) 
 
Horizontal stretch and vertical shift. 
E)

Horizontal stretch and vertical shift.

Question 2

Use long division to divide. $$\left( 6 x ^ { 3 } - 12 x ^ { 2 } + 9 x - 18 \right) \div ( 3 x - 3 )$$

Accepted Answer

A)  $2 x ^ { 2 } + 2 x - 6 , x \neq - 3$ 
B)  $- 2 x ^ { 2 } - 2 x + 6 , x \neq - 3$ 
C)  $2 x ^ { 2 } - 2 x - 6 , x \neq - 3$ 
D)  $2 x ^ { 2 } - 2 x + 6 , x \neq - 3$ 
E)  $2 x ^ { 2 } + 2 x + 6 , x \neq - 3$ 
A)  $2 x ^ { 2 } + 2 x - 6 , x \neq - 3$ 
B)  $- 2 x ^ { 2 } - 2 x + 6 , x \neq - 3$ 
C)  $2 x ^ { 2 } - 2 x - 6 , x \neq - 3$ 
D)  $2 x ^ { 2 } - 2 x + 6 , x \neq - 3$ 
E)  $2 x ^ { 2 } + 2 x + 6 , x \neq - 3$

Question 3

Find the domain of $x$ in the expression. Use a graphing utility to verify your result. $\sqrt { 25 - 16 x ^ { 2 } }$

Accepted Answer

A)  $\left[ \frac { 5 } { 4 } , \frac { 5 } { 4 } \right]$ 
B)  $\left[ - \frac { 5 } { 4 } , - \frac { 5 } { 4 } \right]$ 
C)  $\left[ - \frac { 4 } { 5 } , \frac { 4 } { 5 } \right]$ 
D)  $\left[ - \frac { 5 } { 4 } , \frac { 5 } { 4 } \right]$ 
E)  $\left[ - \frac { 4 } { 5 } , - \frac { 4 } { 5 } \right]$ 
A)  $\left[ \frac { 5 } { 4 } , \frac { 5 } { 4 } \right]$ 
B)  $\left[ - \frac { 5 } { 4 } , - \frac { 5 } { 4 } \right]$ 
C)  $\left[ - \frac { 4 } { 5 } , \frac { 4 } { 5 } \right]$ 
D)  $\left[ - \frac { 5 } { 4 } , \frac { 5 } { 4 } \right]$ 
E)  $\left[ - \frac { 4 } { 5 } , - \frac { 4 } { 5 } \right]$

Question 4

Write the standard form of the equation of the parabola that has a vertex at $( - 8,3 )$ and passes through the point $( 5 , - 5 )$

Accepted Answer

A) $f ( x ) = - \frac { 1 } { 8 } ( x - 8 ) ^ { 2 } + 3$ 
B)  $f ( x ) = \frac { 3 } { 5 } ( x - 3 ) ^ { 2 } - 5$ 
C)  $f ( x ) = - \frac { 8 } { 169 } ( x + 8 ) ^ { 2 } + 3$ 
D)  $f ( x ) = \frac { 3 } { 64 } ( x - 3 ) ^ { 2 } - 5$ 
E)  $f ( x ) = - \frac { 5 } { 169 } ( x + 8 ) ^ { 2 } + 5$ 
A) $f ( x ) = - \frac { 1 } { 8 } ( x - 8 ) ^ { 2 } + 3$ 
B)  $f ( x ) = \frac { 3 } { 5 } ( x - 3 ) ^ { 2 } - 5$ 
C)  $f ( x ) = - \frac { 8 } { 169 } ( x + 8 ) ^ { 2 } + 3$ 
D)  $f ( x ) = \frac { 3 } { 64 } ( x - 3 ) ^ { 2 } - 5$ 
E)  $f ( x ) = - \frac { 5 } { 169 } ( x + 8 ) ^ { 2 } + 5$

Question 5

Use long division to divide. $$\left( x ^ { 4 } + 7 x ^ { 3 } + 12 x ^ { 2 } - x - 3 \right) \div ( x + 3 )$$

Accepted Answer

A)  $x ^ { 3 } + 4 x ^ { 2 } + 1$ 
B)  $x ^ { 3 } - 4 x ^ { 2 } - 1$ 
C)  $x ^ { 3 } + 4 x ^ { 2 } + 1$. 
D)  $x ^ { 3 } - 4 x ^ { 2 } + 1$. 
E)  $x ^ { 3 } + 4 x ^ { 2 } - 1$. 
A)  $x ^ { 3 } + 4 x ^ { 2 } + 1$ 
B)  $x ^ { 3 } - 4 x ^ { 2 } - 1$ 
C)  $x ^ { 3 } + 4 x ^ { 2 } + 1$. 
D)  $x ^ { 3 } - 4 x ^ { 2 } + 1$. 
E)  $x ^ { 3 } + 4 x ^ { 2 } - 1$.

Question 6

Perform the operation and write the result in standard form. 
$\frac { 4 } { 1 + i } - \frac { 5 } { 1 - i }$

Accepted Answer

A)  $- \frac { 1 } { 2 } + \frac { 2 } { 9 } i$ 
B)  $- \frac { 1 } { 2 } - \frac { 2 } { 9 } i$ 
C)  $- \frac { 1 } { 2 } + \frac { 9 } { 2 } i$ 
D)  $\frac { 9 } { 2 } - \frac { 1 } { 2 } i$ 
E)  $- \frac { 1 } { 2 } - \frac { 9 } { 2 } i$ 
A)  $- \frac { 1 } { 2 } + \frac { 2 } { 9 } i$ 
B)  $- \frac { 1 } { 2 } - \frac { 2 } { 9 } i$ 
C)  $- \frac { 1 } { 2 } + \frac { 9 } { 2 } i$ 
D)  $\frac { 9 } { 2 } - \frac { 1 } { 2 } i$ 
E)  $- \frac { 1 } { 2 } - \frac { 9 } { 2 } i$

Question 7

Select the graph of the function and determine the zeros of the polynomial. $f ( x ) = x ^ { 3 } - 4 x$

Accepted Answer

A)  $0,2 , - 2$
  
B)  $0,2,-2$
  
C)  $2 , - 2$
  
D) 
$2 , - 2$
  
E)  $0,2,-2$
  
A)  $0,2 , - 2$
  
B)  $0,2,-2$
  
C)  $2 , - 2$
  
D) 
$2 , - 2$
  
E)  $0,2,-2$

Question 8

Select the correct graph of the following function. $$f ( x ) = \frac { x ^ { 2 } } { 2 x + 1 }$$

Accepted Answer

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

Question 9

Select the graph of the function and determine the zeros of the polynomial. $f ( x ) = x ^ { 3 } - 4 x ^ { 2 }$

Accepted Answer

A) 0,4
  
B)  $0 , - 4$
  
C) 0,4
  
D) $4 , - 4$
  
E) 
$0,4 , - 4$
  
A) 0,4
  
B)  $0 , - 4$
  
C) 0,4
  
D) $4 , - 4$
  
E) 
$0,4 , - 4$

Question 10

Determine the equations of any horizontal and vertical asymptotes of $$f ( x ) = \frac { x ^ { 2 } + 5 x + 6 } { x ^ { 3 } + 3 x ^ { 2 } - x - 3 }$$

Accepted Answer

A)  horizontal: $y = 0$; vertical: $x = 1$ and $x = - 3$ 
B)  horizontal: $y = 1$; vertical: $x = - 3$ 
C)  horizontal: $y = 0$; vertical: $x = - 1$ and $x = 1$ 
D)  horizontal: none; vertical: none 
E)  horizontal: $y = 0$; vertical: $x = - 3$ and $x = - 2$ 
A)  horizontal: $y = 0$; vertical: $x = 1$ and $x = - 3$ 
B)  horizontal: $y = 1$; vertical: $x = - 3$ 
C)  horizontal: $y = 0$; vertical: $x = - 1$ and $x = 1$ 
D)  horizontal: none; vertical: none 
E)  horizontal: $y = 0$; vertical: $x = - 3$ and $x = - 2$

Question 11

Use synthetic division to divide. $$\left( - 8 + 5 x ^ { 3 } - 14 x + 17 x ^ { 2 } \right) \div ( x + 4 )$$

Accepted Answer

A)  $5 x ^ { 2 } - 3 x - 2$ 
B)  $5 x ^ { 2 } + 22 x + 10$ 
C)  $5 x ^ { 2 } - 2 x + 8$ 
D)  $5 x ^ { 2 } + 3 x - 5$ 
E)  $5 x ^ { 2 } - x - 4$ 
A)  $5 x ^ { 2 } - 3 x - 2$ 
B)  $5 x ^ { 2 } + 22 x + 10$ 
C)  $5 x ^ { 2 } - 2 x + 8$ 
D)  $5 x ^ { 2 } + 3 x - 5$ 
E)  $5 x ^ { 2 } - x - 4$

Question 12

Select the correct graph of the following function. 
$f ( x ) = 5 x ^ { 3 } + x ^ { 2 } - 8 x + 2$

Accepted Answer

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

Question 13

$\text { If } x = \sqrt { 3 } \text { is a root of } x ^ { 3 } - x ^ { 2 } - 3 x + 3 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Accepted Answer

A)  $( x + 1 ) ( x + \sqrt { 3 } ) ^ { 2 } ; - 1 , \sqrt { 3 }$ 
B)  $( x + 1 ) ^ { 2 } ( x - \sqrt { 3 } ) ; - 1 , \sqrt { 3 }$ 
C)  $( x + 1 ) ( x + \sqrt { 3 } ) ^ { 2 } ; 1 , - \sqrt { 3 }$ 
D)  $( x + 1 ) ( x - \sqrt { 3 } ) ^ { 2 } ; - 1 , \sqrt { 3 }$ 
E)  $( x - 1 ) ( x - \sqrt { 3 } ) ( x + \sqrt { 3 } ) ; 1 , \sqrt { 3 } , - \sqrt { 3 }$ 
A)  $( x + 1 ) ( x + \sqrt { 3 } ) ^ { 2 } ; - 1 , \sqrt { 3 }$ 
B)  $( x + 1 ) ^ { 2 } ( x - \sqrt { 3 } ) ; - 1 , \sqrt { 3 }$ 
C)  $( x + 1 ) ( x + \sqrt { 3 } ) ^ { 2 } ; 1 , - \sqrt { 3 }$ 
D)  $( x + 1 ) ( x - \sqrt { 3 } ) ^ { 2 } ; - 1 , \sqrt { 3 }$ 
E)  $( x - 1 ) ( x - \sqrt { 3 } ) ( x + \sqrt { 3 } ) ; 1 , \sqrt { 3 } , - \sqrt { 3 }$

Question 14

Simplify the complex number and write it in standard form. $\frac { 1 } { ( 6 i ) ^ { 3 } }$

Accepted Answer

A)  $\frac { 1 } { 6 } i$ 
B) $- \frac { 1 } { 216 } i$ 
C)  $\frac { 1 } { 216 } i$ 
D)  $- \frac { 1 } { 6 } i$ 
E)  $216 i$ 
A)  $\frac { 1 } { 6 } i$ 
B) $- \frac { 1 } { 216 } i$ 
C)  $\frac { 1 } { 216 } i$ 
D)  $- \frac { 1 } { 6 } i$ 
E)  $216 i$

Question 15

Simplify the rational expression, $\frac { x ^ { 4 } + 5 x ^ { 3 } - 11 x ^ { 2 } - 33 x - 18 } { x ^ { 2 } + 2 x + 1 }$ , by using long division or synthetic division.

Accepted Answer

A)  $- x ^ { 2 } - 9 x - 18$ 
B)  $x ^ { 2 } - 2 x - 3$ 
C)  $- x ^ { 2 } - 6 x + 36$ 
D)  $x ^ { 2 } + 3 x - 18$ 
E)  $x ^ { 2 } + 9 x + 36$ 
A)  $- x ^ { 2 } - 9 x - 18$ 
B)  $x ^ { 2 } - 2 x - 3$ 
C)  $- x ^ { 2 } - 6 x + 36$ 
D)  $x ^ { 2 } + 3 x - 18$ 
E)  $x ^ { 2 } + 9 x + 36$

Question 16

Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate. $\sqrt { - 25 }$

Accepted Answer

A)  $- i , 25$ 
B)  $- 5 i , 25$ 
C)  $5 i , 25$ 
D)  $625 i , 25$ 
E)  $- 24 i , 25$ 
A)  $- i , 25$ 
B)  $- 5 i , 25$ 
C)  $5 i , 25$ 
D)  $625 i , 25$ 
E)  $- 24 i , 25$

Question 17

Select the graph of the function $y = x ^ { 2 } - 1$ . Compare the graph of this function with the graph of $y = x ^ { 2 }$

Accepted Answer

A) 
 
Horizontal stretch and vertical shift. 
B) 
 
Horizontal stretch and vertical shift. 
C) 
 
Horizontal stretch and vertical shift. 
D) 
 
Horizontal stretch and vertical shift. 
E) 
 
Horizontal stretch and vertical shift. 
A) 
 
Horizontal stretch and vertical shift. 
B) 
 
Horizontal stretch and vertical shift. 
C) 
 
Horizontal stretch and vertical shift. 
D) 
 
Horizontal stretch and vertical shift. 
E) 
 
Horizontal stretch and vertical shift.

Question 18

Use the position equation $s = - 14 t ^ { 2 } + v _ { 0 } t + s _ { 0 }$ , where $S$ represents the height of an object (in feet), $V _ { 0 }$ represents the initial velocity of the object (in feet per second), $S _ { 0 }$ represents the Initial height of the object (in feet), and $t$ represents the time (in seconds).
A projectile is fired straight upward from ground level $\left( s _ { 0 } = 0 \right)$ with an initial velocity of $112$ feet Per second. At what instant will it be back at ground level?

Accepted Answer

A)  $t = 10 \mathrm { Sec }$ 
B)  $t = 8 \mathrm { Sec }$ 
C)  $t = 7 \mathrm { Sec }$ 
D)  $t = 6 \mathrm { Sec }$ 
E)  $t = 9 \mathrm { Sec }$ 
A)  $t = 10 \mathrm { Sec }$ 
B)  $t = 8 \mathrm { Sec }$ 
C)  $t = 7 \mathrm { Sec }$ 
D)  $t = 6 \mathrm { Sec }$ 
E)  $t = 9 \mathrm { Sec }$

Question 19

Select the graph of the function $y = - 3 x ^ { 2 }$ . Compare the graph of this function with the graph of $y = x ^ { 2 }$

Accepted Answer

A) 
 
Vertical shrink 
B) 
 
Vertical stretch 
C) 
 
Vertical shrink and reflection in $x$-axis 
D) 
 
Reflection in $x$-axis 
E) 
 
Vertical stretch and reflection in $x$-axis 
A) 
 
Vertical shrink 
B) 
 
Vertical stretch 
C) 
 
Vertical shrink and reflection in $x$-axis 
D) 
 
Reflection in $x$-axis 
E) 
 
Vertical stretch and reflection in $x$-axis

Question 20

Solve the inequality and graph the solution on the real number line. $$\frac { x ^ { 2 } + x - 12 } { x } \geq 0$$

Accepted Answer

A)  $[ - 4,0 ) \cap [ 3 , \infty )$
  
B)  $[ 4,0 ) \cup [ 3 , \infty )$
  
C)  $[ 4,0 ) \cup [ - 3 , \infty )$
  
D)  $[ - 4,0 ) \cap [ - 3 , \infty )$
  
E)  $[ - 4,0 ) \cup [ 3 , \infty )$
  
A)  $[ - 4,0 ) \cap [ 3 , \infty )$
  
B)  $[ 4,0 ) \cup [ 3 , \infty )$
  
C)  $[ 4,0 ) \cup [ - 3 , \infty )$
  
D)  $[ - 4,0 ) \cap [ - 3 , \infty )$
  
E)  $[ - 4,0 ) \cup [ 3 , \infty )$

Select the graph of the function $y = ( x / 3 ) ^ { 2 } - 5$ . Compare the graph of this function with the graph of $y = x ^ { 2 }$

Use long division to divide. $\left( 6 x ^ { 3 } - 12 x ^ { 2 } + 9 x - 18 \right) \div ( 3 x - 3 )$

Find the domain of $x$ in the expression. Use a graphing utility to verify your result. $\sqrt { 25 - 16 x ^ { 2 } }$

Write the standard form of the equation of the parabola that has a vertex at $( - 8,3 )$ and passes through the point $( 5 , - 5 )$

Use long division to divide. $\left( x ^ { 4 } + 7 x ^ { 3 } + 12 x ^ { 2 } - x - 3 \right) \div ( x + 3 )$

Perform the operation and write the result in standard form. $\frac { 4 } { 1 + i } - \frac { 5 } { 1 - i }$

Select the graph of the function and determine the zeros of the polynomial. $f ( x ) = x ^ { 3 } - 4 x$

Select the correct graph of the following function. $f ( x ) = \frac { x ^ { 2 } } { 2 x + 1 }$

Select the graph of the function and determine the zeros of the polynomial. $f ( x ) = x ^ { 3 } - 4 x ^ { 2 }$

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x ^ { 2 } + 5 x + 6 } { x ^ { 3 } + 3 x ^ { 2 } - x - 3 }$

Use synthetic division to divide. $\left( - 8 + 5 x ^ { 3 } - 14 x + 17 x ^ { 2 } \right) \div ( x + 4 )$

Select the correct graph of the following function. $f ( x ) = 5 x ^ { 3 } + x ^ { 2 } - 8 x + 2$

$\text { If } x = \sqrt { 3 } \text { is a root of } x ^ { 3 } - x ^ { 2 } - 3 x + 3 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Simplify the complex number and write it in standard form. $\frac { 1 } { ( 6 i ) ^ { 3 } }$

Simplify the rational expression, $\frac { x ^ { 4 } + 5 x ^ { 3 } - 11 x ^ { 2 } - 33 x - 18 } { x ^ { 2 } + 2 x + 1 }$ , by using long division or synthetic division.

Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate. $\sqrt { - 25 }$

Select the graph of the function $y = x ^ { 2 } - 1$ . Compare the graph of this function with the graph of $y = x ^ { 2 }$

Select the graph of the function $y = - 3 x ^ { 2 }$ . Compare the graph of this function with the graph of $y = x ^ { 2 }$

Solve the inequality and graph the solution on the real number line. $\frac { x ^ { 2 } + x - 12 } { x } \geq 0$

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Topics in Analytic Geometry

Filters

Exam 2: Polynomial and Rational Functions

Select the graph of the function y=(x/3)2−5y = ( x / 3 ) ^ { 2 } - 5y=(x/3)2−5 . Compare the graph of this function with the graph of y=x2y = x ^ { 2 }y=x2

Use long division to divide. (6x3−12x2+9x−18)÷(3x−3)\left( 6 x ^ { 3 } - 12 x ^ { 2 } + 9 x - 18 \right) \div ( 3 x - 3 )(6x3−12x2+9x−18)÷(3x−3)

Find the domain of xxx in the expression. Use a graphing utility to verify your result. 25−16x2\sqrt { 25 - 16 x ^ { 2 } }25−16x2​

Write the standard form of the equation of the parabola that has a vertex at (−8,3)( - 8,3 )(−8,3) and passes through the point (5,−5)( 5 , - 5 )(5,−5)

Use long division to divide. (x4+7x3+12x2−x−3)÷(x+3)\left( x ^ { 4 } + 7 x ^ { 3 } + 12 x ^ { 2 } - x - 3 \right) \div ( x + 3 )(x4+7x3+12x2−x−3)÷(x+3)

Perform the operation and write the result in standard form. 41+i−51−i\frac { 4 } { 1 + i } - \frac { 5 } { 1 - i }1+i4​−1−i5​

Select the graph of the function and determine the zeros of the polynomial. f(x)=x3−4xf ( x ) = x ^ { 3 } - 4 xf(x)=x3−4x

Select the correct graph of the following function. f(x)=x22x+1f ( x ) = \frac { x ^ { 2 } } { 2 x + 1 }f(x)=2x+1x2​

Select the graph of the function and determine the zeros of the polynomial. f(x)=x3−4x2f ( x ) = x ^ { 3 } - 4 x ^ { 2 }f(x)=x3−4x2

Determine the equations of any horizontal and vertical asymptotes of f(x)=x2+5x+6x3+3x2−x−3f ( x ) = \frac { x ^ { 2 } + 5 x + 6 } { x ^ { 3 } + 3 x ^ { 2 } - x - 3 }f(x)=x3+3x2−x−3x2+5x+6​

Use synthetic division to divide. (−8+5x3−14x+17x2)÷(x+4)\left( - 8 + 5 x ^ { 3 } - 14 x + 17 x ^ { 2 } \right) \div ( x + 4 )(−8+5x3−14x+17x2)÷(x+4)

Select the correct graph of the following function. f(x)=5x3+x2−8x+2f ( x ) = 5 x ^ { 3 } + x ^ { 2 } - 8 x + 2f(x)=5x3+x2−8x+2

If x=3 is a root of x3−x2−3x+3=0\text { If } x = \sqrt { 3 } \text { is a root of } x ^ { 3 } - x ^ { 2 } - 3 x + 3 = 0 If x=3​ is a root of x3−x2−3x+3=0 , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Simplify the complex number and write it in standard form. 1(6i)3\frac { 1 } { ( 6 i ) ^ { 3 } }(6i)31​

Simplify the rational expression, x4+5x3−11x2−33x−18x2+2x+1\frac { x ^ { 4 } + 5 x ^ { 3 } - 11 x ^ { 2 } - 33 x - 18 } { x ^ { 2 } + 2 x + 1 }x2+2x+1x4+5x3−11x2−33x−18​ , by using long division or synthetic division.

Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate. −25\sqrt { - 25 }−25​

Select the graph of the function y=x2−1y = x ^ { 2 } - 1y=x2−1 . Compare the graph of this function with the graph of y=x2y = x ^ { 2 }y=x2

Select the graph of the function y=−3x2y = - 3 x ^ { 2 }y=−3x2 . Compare the graph of this function with the graph of y=x2y = x ^ { 2 }y=x2

Solve the inequality and graph the solution on the real number line. x2+x−12x≥0\frac { x ^ { 2 } + x - 12 } { x } \geq 0xx2+x−12​≥0

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Topics in Analytic Geometry

Filters

Select the graph of the function $y = ( x / 3 ) ^ { 2 } - 5$ . Compare the graph of this function with the graph of $y = x ^ { 2 }$

Use long division to divide. $\left( 6 x ^ { 3 } - 12 x ^ { 2 } + 9 x - 18 \right) \div ( 3 x - 3 )$

Find the domain of $x$ in the expression. Use a graphing utility to verify your result. $\sqrt { 25 - 16 x ^ { 2 } }$

Write the standard form of the equation of the parabola that has a vertex at $( - 8,3 )$ and passes through the point $( 5 , - 5 )$

Use long division to divide. $\left( x ^ { 4 } + 7 x ^ { 3 } + 12 x ^ { 2 } - x - 3 \right) \div ( x + 3 )$

Perform the operation and write the result in standard form. $\frac { 4 } { 1 + i } - \frac { 5 } { 1 - i }$

Select the graph of the function and determine the zeros of the polynomial. $f ( x ) = x ^ { 3 } - 4 x$

Select the correct graph of the following function. $f ( x ) = \frac { x ^ { 2 } } { 2 x + 1 }$

Select the graph of the function and determine the zeros of the polynomial. $f ( x ) = x ^ { 3 } - 4 x ^ { 2 }$

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x ^ { 2 } + 5 x + 6 } { x ^ { 3 } + 3 x ^ { 2 } - x - 3 }$

Use synthetic division to divide. $\left( - 8 + 5 x ^ { 3 } - 14 x + 17 x ^ { 2 } \right) \div ( x + 4 )$

Select the correct graph of the following function. $f ( x ) = 5 x ^ { 3 } + x ^ { 2 } - 8 x + 2$

$\text { If } x = \sqrt { 3 } \text { is a root of } x ^ { 3 } - x ^ { 2 } - 3 x + 3 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Simplify the complex number and write it in standard form. $\frac { 1 } { ( 6 i ) ^ { 3 } }$

Simplify the rational expression, $\frac { x ^ { 4 } + 5 x ^ { 3 } - 11 x ^ { 2 } - 33 x - 18 } { x ^ { 2 } + 2 x + 1 }$ , by using long division or synthetic division.

Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate. $\sqrt { - 25 }$

Select the graph of the function $y = x ^ { 2 } - 1$ . Compare the graph of this function with the graph of $y = x ^ { 2 }$

Select the graph of the function $y = - 3 x ^ { 2 }$ . Compare the graph of this function with the graph of $y = x ^ { 2 }$

Solve the inequality and graph the solution on the real number line. $\frac { x ^ { 2 } + x - 12 } { x } \geq 0$