Question 1

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f(x) = 6x3 - 5x2 + 6x - 6.

Accepted Answer

A) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real 
B) no positive reals; no negative reals 
C) 3 positive reals or 1 positive real; 1 negative real 
D) 1 positive real; 3 negative reals or 1 negative real 
E) 3 positive reals or 1 positive real; no negative reals 
A) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real 
B) no positive reals; no negative reals 
C) 3 positive reals or 1 positive real; 1 negative real 
D) 1 positive real; 3 negative reals or 1 negative real 
E) 3 positive reals or 1 positive real; no negative reals

Question 2

Determine the zeros (if any) of the rational function $g ( x ) = \frac { x ^ { 3 } - 64 } { x ^ { 2 } + 6 }$ .

Accepted Answer

A)  $x = - \sqrt { 6 } , x = \sqrt { 6 } , x = 4$ 
B) no zeros 
C)  x = -4, x = 4 
D)  x = 4 
E)   $x = - \sqrt { 6 } , x = \sqrt { 6 } , x = - 4 , x = 4$ 
A)  $x = - \sqrt { 6 } , x = \sqrt { 6 } , x = 4$ 
B) no zeros 
C)  x = -4, x = 4 
D)  x = 4 
E)   $x = - \sqrt { 6 } , x = \sqrt { 6 } , x = - 4 , x = 4$

Question 3

Find all zeros of the function f(x) = x2(x + 1)(x3 - 64).

Accepted Answer

A) x = 0, 1, -4 
B) x = 0, -1, 4 
C) x = -1, 64 
D) x = 1, -64 
E) x = 0, -1, 4, $- 2 - 2 \sqrt { 3 } i$ , $- 2 + 2 \sqrt { 3 } i$ 
A) x = 0, 1, -4 
B) x = 0, -1, 4 
C) x = -1, 64 
D) x = 1, -64 
E) x = 0, -1, 4, $- 2 - 2 \sqrt { 3 } i$ , $- 2 + 2 \sqrt { 3 } i$

Question 4

Graph the quadratic function. ​
F (x) = - 4x2 + 2
​

Accepted Answer

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

Question 5

Perform the operation and write the result in standard form. 
 $( 8 - 7 i ) ^ { 2 }$

Accepted Answer

A)   $15 - 112 i$ 
B)   $- 15 - 112 i$ 
C)   $15 + 112 i$ 
D)   $17 - 112 i$ 
E)  $- 15 + 112 i$ 
A)   $15 - 112 i$ 
B)   $- 15 - 112 i$ 
C)   $15 + 112 i$ 
D)   $17 - 112 i$ 
E)  $- 15 + 112 i$

Question 6

Find a polynomial function with real coefficients that has the given zeros. ​
1, 3i
​

Accepted Answer

A) x3 - x2 - 9x - 9 
B) x3 + x2 + 9x - 9 
C) x3 - x2 + 9x - 9 
D) x3 + x2 + 9x + 9 
E) x3 - x2 + 9x + 9 
A) x3 - x2 - 9x - 9 
B) x3 + x2 + 9x - 9 
C) x3 - x2 + 9x - 9 
D) x3 + x2 + 9x + 9 
E) x3 - x2 + 9x + 9

Question 7

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f(x) = 6x3 + 3x2 + 3x + 4.

Accepted Answer

A) no positive reals; no negative reals 
B) 1 positive real; 3 negative reals or 1 negative real 
C) 0 positive real; 3 negative reals or 1 negative real 
D) 3 positive reals or 1 positive real; no negative reals 
E) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real 
A) no positive reals; no negative reals 
B) 1 positive real; 3 negative reals or 1 negative real 
C) 0 positive real; 3 negative reals or 1 negative real 
D) 3 positive reals or 1 positive real; no negative reals 
E) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real

Question 8

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality.  
Equation: $y = x ^ { 3 } - x ^ { 2 } - 16 x + 16$  
Inequality: $y \leq 0$

Accepted Answer

A)       $\begin{array} { l } 
\infty < x \leq 4 \
1 \leq x \leq 4
\end{array}$ 
B)      $\begin{array} { l } 
\infty < x \leq - 4 \
1 \leq x \leq 4
\end{array}$ 
C)      $\begin{array} { l } 
- \infty < x \leq - 4 \
- 1 \leq x \leq - 4
\end{array}$ 
D)     $\begin{array} { l } 
- \infty < x \leq - 4 \
1 \leq x \leq 4
\end{array}$ 
E)       $- \infty < x \leq 4$ 
A)       $\begin{array} { l } 
\infty < x \leq 4 \
1 \leq x \leq 4
\end{array}$ 
B)      $\begin{array} { l } 
\infty < x \leq - 4 \
1 \leq x \leq 4
\end{array}$ 
C)      $\begin{array} { l } 
- \infty < x \leq - 4 \
- 1 \leq x \leq - 4
\end{array}$ 
D)     $\begin{array} { l } 
- \infty < x \leq - 4 \
1 \leq x \leq 4
\end{array}$ 
E)       $- \infty < x \leq 4$

Question 9

The game commission introduces 100 deer into newly acquired state game lands.The population N of the herd is modeled by   $N = \frac { 22 ( 5 + 3 t ) } { 1 + 0.04 t } , t \geq 0$  
Where t is the time in years.
Select the correct graph of this model.

Accepted Answer

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

Question 10

Write the complex number in standard form. 
$( 4 + \sqrt { - 6 } ) ( 6 - \sqrt { - 14 } )$

Accepted Answer

A) (24 - $2 \sqrt { 21 }$ ) - (6 $\sqrt { 6 }$ - 4 $\sqrt { 14 }$ )i 
B) (24 + $2 \sqrt { 21 }$ ) + (6 $\sqrt { 6 }$ - 4 $\sqrt { 14 }$ )i 
C) (24 - $2 \sqrt { 21 }$ ) + (6 $\sqrt { 6 }$ - 4 $\sqrt { 14 }$ )i 
D) (24 + $2 \sqrt { 21 }$ ) - (6 $\sqrt { 6 }$ - 4 $\sqrt { 14 }$ )i 
E) (24 + $2 \sqrt { 21 }$ ) + (6 $\sqrt { 6 }$ + 4 $\sqrt { 14 }$ )i 
A) (24 - $2 \sqrt { 21 }$ ) - (6 $\sqrt { 6 }$ - 4 $\sqrt { 14 }$ )i 
B) (24 + $2 \sqrt { 21 }$ ) + (6 $\sqrt { 6 }$ - 4 $\sqrt { 14 }$ )i 
C) (24 - $2 \sqrt { 21 }$ ) + (6 $\sqrt { 6 }$ - 4 $\sqrt { 14 }$ )i 
D) (24 + $2 \sqrt { 21 }$ ) - (6 $\sqrt { 6 }$ - 4 $\sqrt { 14 }$ )i 
E) (24 + $2 \sqrt { 21 }$ ) + (6 $\sqrt { 6 }$ + 4 $\sqrt { 14 }$ )i

Question 11

Solve the inequality and graph the solution on the real number line.   $\frac { 4 x - 1 } { x } > 0$

Accepted Answer

A)  $( - \infty , 0 ) \cup \left( \frac { 1 } { 4 } , \infty \right)$   
B)  $( - \infty , 0 ) \cup \left( - \frac { 1 } { 4 } , \infty \right)$     
C)  $( - \infty , 0 ) \cap \left( - \frac { 1 } { 4 } , \frac { 1 } { 4 } \right)$   
D)  $( - \infty , 0 ) \cap \left( \frac { 1 } { 4 } , \infty \right)$   
E)  $( - \infty , 0 ) \cap \left( - \frac { 1 } { 4 } , \infty \right)$   
A)  $( - \infty , 0 ) \cup \left( \frac { 1 } { 4 } , \infty \right)$   
B)  $( - \infty , 0 ) \cup \left( - \frac { 1 } { 4 } , \infty \right)$     
C)  $( - \infty , 0 ) \cap \left( - \frac { 1 } { 4 } , \frac { 1 } { 4 } \right)$   
D)  $( - \infty , 0 ) \cap \left( \frac { 1 } { 4 } , \infty \right)$   
E)  $( - \infty , 0 ) \cap \left( - \frac { 1 } { 4 } , \infty \right)$

Question 12

Find all rational roots of the equation.  
147x 3 - 98x 2 + 27x - 18 = 0

Accepted Answer

A)  $x = \frac { 2 } { 5 }$ 
B)   $x = \frac { 2 } { 3 }$ 
C)   $x = - \frac { 3 } { 7 } i$ 
D)   $x = \frac { 3 } { 7 } i$ 
A)  $x = \frac { 2 } { 5 }$ 
B)   $x = \frac { 2 } { 3 }$ 
C)   $x = - \frac { 3 } { 7 } i$ 
D)   $x = \frac { 3 } { 7 } i$

Question 13

Write the quotient in standard form.  
  $\frac { 6 + 12 i } { 4 i }$

Accepted Answer

A) 3 - $\frac { 3 } { 2 }$ i 
B) 3 - 3i 
C) 3 $+$ $\frac { 3 } { 2 }$ i 
D) 3i - $\frac { 3 } { 2 }$ 
E) 3i + $\frac { 3 } { 2 }$ 
A) 3 - $\frac { 3 } { 2 }$ i 
B) 3 - 3i 
C) 3 $+$ $\frac { 3 } { 2 }$ i 
D) 3i - $\frac { 3 } { 2 }$ 
E) 3i + $\frac { 3 } { 2 }$

Question 14

Solve the inequality and graph the solution on the real number line. 
$x ^ { 2 } + 5 x + 13 > 0$

Accepted Answer

A) $x \geq - 13$ B) $x \leq 13$ C) $x > 5$ D) $x < - 5$ E) All real numbers A) $x \geq - 13$ B) $x \leq 13$ C) $x > 5$ D) $x < - 5$ E) All real numbers

Question 15

Determine the value that the function f approaches as the magnitude of x increases. 
 $f ( x ) = 3 + \frac { 1 } { x - 4 }$

Accepted Answer

A) 2.75 
B)  3 
C)  1 
D)  4 
E) -0.25 
A) 2.75 
B)  3 
C)  1 
D)  4 
E) -0.25

Question 16

Find vertical and horizontal asymptotes. 
 $f ( x ) = \frac { 9 + 6 x } { 6 + x }$

Accepted Answer

A) Vertical asymptote: x = -6Horizontal asymptote: y = 6 
B) Vertical asymptote: x = 0Horizontal asymptote: y = -6 
C) Vertical asymptote: x = 6Horizontal asymptote: y = -6 
D) Vertical asymptote: x = 0Horizontal asymptote: y = 6 
E) Vertical asymptote: x = -6Horizontal asymptote: y = 0 
A) Vertical asymptote: x = -6Horizontal asymptote: y = 6 
B) Vertical asymptote: x = 0Horizontal asymptote: y = -6 
C) Vertical asymptote: x = 6Horizontal asymptote: y = -6 
D) Vertical asymptote: x = 0Horizontal asymptote: y = 6 
E) Vertical asymptote: x = -6Horizontal asymptote: y = 0

Question 17

Select the graph of the quadratic function. 
 $f ( x ) = x ^ { 2 } - 5 x$

Accepted Answer

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

Question 18

Select the correct graph for the following rational function. 
 $f ( x ) = \frac { 11 } { x - 8 }$

Accepted Answer

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

Question 19

Select the correct graph of the following function.   $f ( x ) = \frac { x ^ { 2 } + 6 } { x }$

Accepted Answer

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

Question 20

The graph of the function g(x) is a translation of the graph of f (x) = x 3.Graph the function g(x) = (x - 1) 3. ​

Accepted Answer

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

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f(x) = 6x³ - 5x² + 6x - 6.

Determine the zeros (if any) of the rational function $g ( x ) = \frac { x ^ { 3 } - 64 } { x ^ { 2 } + 6 }$ .

Find all zeros of the function f(x) = x²(x + 1)(x³ - 64).

Graph the quadratic function. F (x) = - 4x² + 2

Perform the operation and write the result in standard form. $( 8 - 7 i ) ^ { 2 }$

Find a polynomial function with real coefficients that has the given zeros. 1, 3i

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f(x) = 6x³ + 3x² + 3x + 4.

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. Equation: $y = x ^ { 3 } - x ^ { 2 } - 16 x + 16$ Inequality: $y \leq 0$

The game commission introduces 100 deer into newly acquired state game lands.The population N of the herd is modeled by $N = \frac { 22 ( 5 + 3 t ) } { 1 + 0.04 t } , t \geq 0$ Where t is the time in years. Select the correct graph of this model.

Write the complex number in standard form. $( 4 + \sqrt { - 6 } ) ( 6 - \sqrt { - 14 } )$

Solve the inequality and graph the solution on the real number line. $\frac { 4 x - 1 } { x } > 0$

Find all rational roots of the equation. 147x ³ - 98x ² + 27x - 18 = 0

Write the quotient in standard form. $\frac { 6 + 12 i } { 4 i }$

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } + 5 x + 13 > 0$

Determine the value that the function f approaches as the magnitude of x increases. $f ( x ) = 3 + \frac { 1 } { x - 4 }$

Find vertical and horizontal asymptotes. $f ( x ) = \frac { 9 + 6 x } { 6 + x }$

Select the graph of the quadratic function. $f ( x ) = x ^ { 2 } - 5 x$

Select the correct graph for the following rational function. $f ( x ) = \frac { 11 } { x - 8 }$

Select the correct graph of the following function. $f ( x ) = \frac { x ^ { 2 } + 6 } { x }$

The graph of the function g(x) is a translation of the graph of f (x) = x ³.Graph the function g(x) = (x - 1) ³.

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 2: Polynomial and Rational Functions

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f(x) = 6x3 - 5x2 + 6x - 6.

Determine the zeros (if any) of the rational function g(x)=x3−64x2+6g ( x ) = \frac { x ^ { 3 } - 64 } { x ^ { 2 } + 6 }g(x)=x2+6x3−64​ .

Find all zeros of the function f(x) = x2(x + 1)(x3 - 64).

Graph the quadratic function. ​ F (x) = - 4x2 + 2 ​

Perform the operation and write the result in standard form. (8−7i)2( 8 - 7 i ) ^ { 2 }(8−7i)2

Find a polynomial function with real coefficients that has the given zeros. ​ 1, 3i ​

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f(x) = 6x3 + 3x2 + 3x + 4.

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. Equation: y=x3−x2−16x+16y = x ^ { 3 } - x ^ { 2 } - 16 x + 16y=x3−x2−16x+16 Inequality: y≤0y \leq 0y≤0

The game commission introduces 100 deer into newly acquired state game lands.The population N of the herd is modeled by N=22(5+3t)1+0.04t,t≥0N = \frac { 22 ( 5 + 3 t ) } { 1 + 0.04 t } , t \geq 0N=1+0.04t22(5+3t)​,t≥0 Where t is the time in years. Select the correct graph of this model.

Write the complex number in standard form. (4+−6)(6−−14)( 4 + \sqrt { - 6 } ) ( 6 - \sqrt { - 14 } )(4+−6​)(6−−14​)

Solve the inequality and graph the solution on the real number line. 4x−1x>0\frac { 4 x - 1 } { x } > 0x4x−1​>0

Find all rational roots of the equation. 147x 3 - 98x 2 + 27x - 18 = 0

Write the quotient in standard form. 6+12i4i\frac { 6 + 12 i } { 4 i }4i6+12i​

Solve the inequality and graph the solution on the real number line. x2+5x+13>0x ^ { 2 } + 5 x + 13 > 0x2+5x+13>0

Determine the value that the function f approaches as the magnitude of x increases. f(x)=3+1x−4f ( x ) = 3 + \frac { 1 } { x - 4 }f(x)=3+x−41​

Find vertical and horizontal asymptotes. f(x)=9+6x6+xf ( x ) = \frac { 9 + 6 x } { 6 + x }f(x)=6+x9+6x​

Select the graph of the quadratic function. f(x)=x2−5xf ( x ) = x ^ { 2 } - 5 xf(x)=x2−5x

Select the correct graph for the following rational function. f(x)=11x−8f ( x ) = \frac { 11 } { x - 8 }f(x)=x−811​

Select the correct graph of the following function. f(x)=x2+6xf ( x ) = \frac { x ^ { 2 } + 6 } { x }f(x)=xx2+6​

The graph of the function g(x) is a translation of the graph of f (x) = x 3.Graph the function g(x) = (x - 1) 3. ​

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f(x) = 6x³ - 5x² + 6x - 6.

Determine the zeros (if any) of the rational function $g ( x ) = \frac { x ^ { 3 } - 64 } { x ^ { 2 } + 6 }$ .

Find all zeros of the function f(x) = x²(x + 1)(x³ - 64).

Graph the quadratic function. F (x) = - 4x² + 2

Perform the operation and write the result in standard form. $( 8 - 7 i ) ^ { 2 }$

Find a polynomial function with real coefficients that has the given zeros. 1, 3i

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f(x) = 6x³ + 3x² + 3x + 4.

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. Equation: $y = x ^ { 3 } - x ^ { 2 } - 16 x + 16$ Inequality: $y \leq 0$

The game commission introduces 100 deer into newly acquired state game lands.The population N of the herd is modeled by $N = \frac { 22 ( 5 + 3 t ) } { 1 + 0.04 t } , t \geq 0$ Where t is the time in years. Select the correct graph of this model.

Write the complex number in standard form. $( 4 + \sqrt { - 6 } ) ( 6 - \sqrt { - 14 } )$

Solve the inequality and graph the solution on the real number line. $\frac { 4 x - 1 } { x } > 0$

Find all rational roots of the equation. 147x ³ - 98x ² + 27x - 18 = 0

Write the quotient in standard form. $\frac { 6 + 12 i } { 4 i }$

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } + 5 x + 13 > 0$

Determine the value that the function f approaches as the magnitude of x increases. $f ( x ) = 3 + \frac { 1 } { x - 4 }$

Find vertical and horizontal asymptotes. $f ( x ) = \frac { 9 + 6 x } { 6 + x }$

Select the graph of the quadratic function. $f ( x ) = x ^ { 2 } - 5 x$

Select the correct graph for the following rational function. $f ( x ) = \frac { 11 } { x - 8 }$

Select the correct graph of the following function. $f ( x ) = \frac { x ^ { 2 } + 6 } { x }$

The graph of the function g(x) is a translation of the graph of f (x) = x ³.Graph the function g(x) = (x - 1) ³.