Question 1

Do the operation and express the answer in a + bi form. 
 $( 5 + \sqrt { - 16 } ) ( 4 - \sqrt { - 4 } )$

Accepted Answer

A) 28 - 5 i 
B) - 28 + 6 i 
C) - 5 + 6 i 
D) 5 - 6 i 
E) 28 + 6 i 
A) 28 - 5 i 
B) - 28 + 6 i 
C) - 5 + 6 i 
D) 5 - 6 i 
E) 28 + 6 i

Question 2

Solve the inequality and graph the solution on the real number line.
 $x ^ { 2 } > 2 x + 48$

Accepted Answer

A)  $( - \infty , - 6 ) \cup ( 8 , \infty )$   
B)  $( - \infty , 6 ) \cup ( 8 , \infty )$   
C)  $( - \infty , - 6 ) \cup ( - 8 , - \infty )$   
D)  $( - \infty , - 6 ) \cup ( - 8 , \infty )$   
E)  $( - \infty , 6 ) \cup ( 8 , \infty )$   
A)  $( - \infty , - 6 ) \cup ( 8 , \infty )$   
B)  $( - \infty , 6 ) \cup ( 8 , \infty )$   
C)  $( - \infty , - 6 ) \cup ( - 8 , - \infty )$   
D)  $( - \infty , - 6 ) \cup ( - 8 , \infty )$   
E)  $( - \infty , 6 ) \cup ( 8 , \infty )$

Question 3

A small theater has a seating capacity of 2000.When the ticket price is $20, attendance is 1500.For each $1 decrease in price, attendance increases by 125.Write the revenue R of the theater as a function of ticket price x.

Accepted Answer

A)  $R ( x ) = 125 x ^ { 2 } + 3000 x , 16 \leq x \leq 20$ 
B)  $R ( x ) = - 125 x ^ { 2 } + 1000 x , 16 \leq x \leq 20$ 
C)  $R ( x ) = - 125 x ^ { 3 } + 500 x , 16 \leq x \leq 20$ 
D)  $R ( x ) = - 125 x ^ { 2 } - 350 x , 16 \leq x \leq 20$ 
E)  $R ( x ) = - 125 x ^ { 2 } + 4000 x , 16 \leq x \leq 20$ 
A)  $R ( x ) = 125 x ^ { 2 } + 3000 x , 16 \leq x \leq 20$ 
B)  $R ( x ) = - 125 x ^ { 2 } + 1000 x , 16 \leq x \leq 20$ 
C)  $R ( x ) = - 125 x ^ { 3 } + 500 x , 16 \leq x \leq 20$ 
D)  $R ( x ) = - 125 x ^ { 2 } - 350 x , 16 \leq x \leq 20$ 
E)  $R ( x ) = - 125 x ^ { 2 } + 4000 x , 16 \leq x \leq 20$

Question 4

Solve the inequality and graph the solution on the real number line.   $\frac { 3 x - 5 } { x - 5 } \geq 0$

Accepted Answer

A) ( $- \infty , \frac { 5 } { 3 }$  ] $\text { U } ( 5 , \infty )$   
B) ( $- \infty , \frac { 5 } { 3 }$  ] $\cup ( - 5 , \infty )$   
C) ( $- \infty , - \frac { 5 } { 3 }$  ] $\text { U } ( 5 , \infty )$   
D) ( $- \infty , - \frac { 5 } { 3 }$  ] $\cup ( - 5 , \infty )$   
E) ( $- \infty , \frac { 5 } { 3 }$  ] $\cap ( 5 , \infty )$   
A) ( $- \infty , \frac { 5 } { 3 }$  ] $\text { U } ( 5 , \infty )$   
B) ( $- \infty , \frac { 5 } { 3 }$  ] $\cup ( - 5 , \infty )$   
C) ( $- \infty , - \frac { 5 } { 3 }$  ] $\text { U } ( 5 , \infty )$   
D) ( $- \infty , - \frac { 5 } { 3 }$  ] $\cup ( - 5 , \infty )$   
E) ( $- \infty , \frac { 5 } { 3 }$  ] $\cap ( 5 , \infty )$

Question 5

If x = $\frac { 2 } { 7 }$ is a root of $49 x ^ { 3 } - 126 x ^ { 2 } + 60 x - 8 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Accepted Answer

A)   $( 7 x + 2 ) ^ { 2 } ( x - 2 )$ ; x = $- \frac { 2 } { 7 }$ , 2 
B)  $( 7 x - 2 ) ( x - 2 ) ^ { 2 }$ ; x = $\frac { 2 } { 7 }$ , 2 
C)  $( 7 x + 2 ) ( x - 2 ) ^ { 2 }$ ; x = $- \frac { 2 } { 7 }$ , 2 
D)  $( 7 x - 2 ) ^ { 2 } ( x - 2 )$ ; x = $\frac { 2 } { 7 }$ , 2 
E)  $( 7 x - 2 ) ( 7 x + 2 ) ( x - 2 )$ ; x = $\frac { 2 } { 7 }$ , $- \frac { 2 } { 7 }$ , 2 
A)   $( 7 x + 2 ) ^ { 2 } ( x - 2 )$ ; x = $- \frac { 2 } { 7 }$ , 2 
B)  $( 7 x - 2 ) ( x - 2 ) ^ { 2 }$ ; x = $\frac { 2 } { 7 }$ , 2 
C)  $( 7 x + 2 ) ( x - 2 ) ^ { 2 }$ ; x = $- \frac { 2 } { 7 }$ , 2 
D)  $( 7 x - 2 ) ^ { 2 } ( x - 2 )$ ; x = $\frac { 2 } { 7 }$ , 2 
E)  $( 7 x - 2 ) ( 7 x + 2 ) ( x - 2 )$ ; x = $\frac { 2 } { 7 }$ , $- \frac { 2 } { 7 }$ , 2

Question 6

Which of the following is the graph of the given equation?  
 $f ( x ) = \frac { 2 - x } { x + 3 }$

Accepted Answer

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

Question 7

Find the values of x and y.
​
x + 59i = y - yi
​
x = __________
​
y = __________

Accepted Answer

The answer of Find the values of x and y.
​
x...

Question 8

Solve the inequality $36 x - x ^ { 3 } < 0$ and write the solution set in interval notation.

Accepted Answer

A)  $( - \infty , - 6 ) \cup ( 0,6 )$ 
B)  $( - 6,6 )$ 
C)  $( - \infty , 6 )$ 
D)  $( - 6,0 ) \cup ( 6 , \infty )$ 
E)  $( - \infty , \infty )$ 
A)  $( - \infty , - 6 ) \cup ( 0,6 )$ 
B)  $( - 6,6 )$ 
C)  $( - \infty , 6 )$ 
D)  $( - 6,0 ) \cup ( 6 , \infty )$ 
E)  $( - \infty , \infty )$

Question 9

Use synthetic division to express $P ( x ) = 3 x ^ { 3 } - 10 x ^ { 2 } - 23 x - 35$ in the form (divisor)(quotient) + remainder for the divisor x - 5.

Accepted Answer

A)  $( x - 3 ) \left( 25 x ^ { 2 } + 5 x + 2 \right) - 25$ 
B)  $( x - 5 ) \left( 3 x ^ { 2 } + 5 x + 2 \right) - 25$ 
C)  $( x - 5 ) \left( 3 x ^ { 2 } + 2 \right) - 25$ 
D)  $( x - 5 ) \left( 3 x ^ { 2 } + x + 2 \right)$ 
E) none of these 
A)  $( x - 3 ) \left( 25 x ^ { 2 } + 5 x + 2 \right) - 25$ 
B)  $( x - 5 ) \left( 3 x ^ { 2 } + 5 x + 2 \right) - 25$ 
C)  $( x - 5 ) \left( 3 x ^ { 2 } + 2 \right) - 25$ 
D)  $( x - 5 ) \left( 3 x ^ { 2 } + x + 2 \right)$ 
E) none of these

Question 10

The growth of a red oak tree is approximated by the function 
  $G = - 0.003 t ^ { 3 } + 0.137 t ^ { 2 } + 0.458 t - 0.839$  
Where G is the height of the tree (in feet) and t $( 2 \leq t \leq 34 )$ is its age (in years).
Select the correct graph of the function.

Accepted Answer

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

Question 11

Use long division to divide.  
  $\left( x ^ { 4 } + 7 x ^ { 3 } + 10 x ^ { 2 } - x - 2 \right) \div ( x + 2 )$

Accepted Answer

A)  $x ^ { 3 } + 5 x ^ { 2 } + 1$ 
B)  $x ^ { 3 } - 5 x ^ { 2 } - 1$ 
C)  $x ^ { 3 } + 5 x ^ { 2 } - 1$ 
D)  $x ^ { 2 } + 5 x - 1$ 
E)  $x ^ { 3 } - 5 x ^ { 2 } + 1$ 
A)  $x ^ { 3 } + 5 x ^ { 2 } + 1$ 
B)  $x ^ { 3 } - 5 x ^ { 2 } - 1$ 
C)  $x ^ { 3 } + 5 x ^ { 2 } - 1$ 
D)  $x ^ { 2 } + 5 x - 1$ 
E)  $x ^ { 3 } - 5 x ^ { 2 } + 1$

Question 12

Use the Remainder Theorem and synthetic division to find the function value. 
 $g ( x ) = 3 x ^ { 6 } + 4 x ^ { 4 } - 6 x ^ { 2 } + 4 , \quad g ( 0 )$

Accepted Answer

A) 4.00 
B) 1.00 
C) -1.00 
D) 6.00 
E) 5 
A) 4.00 
B) 1.00 
C) -1.00 
D) 6.00 
E) 5

Question 13

Given $f ( x ) = \frac { x ^ { 2 } + 49 } { x + 7 } , g ( x ) = x - 7$ .Determine the domains of f(x) and g(x).

Accepted Answer

A) Domain of f(x): all real numbers except -7Domain of g(x): all real numbers except 7 
B) Domain of f(x): all real numbersDomain of g(x): all real numbers except 7 
C) Domain of f(x): all real numbersDomain of g(x): all real numbers 
D) Domain of f(x): all real numbers except -7Domain of g(x): all real numbers 
E) Domain of f(x): all real numbers except 7Domain of g(x): all real numbers 
A) Domain of f(x): all real numbers except -7Domain of g(x): all real numbers except 7 
B) Domain of f(x): all real numbersDomain of g(x): all real numbers except 7 
C) Domain of f(x): all real numbersDomain of g(x): all real numbers 
D) Domain of f(x): all real numbers except -7Domain of g(x): all real numbers 
E) Domain of f(x): all real numbers except 7Domain of g(x): all real numbers

Question 14

Find the domain of x in the expression $\sqrt [ 4 ] { x ^ { 3 } - 3 x }$ .

Accepted Answer

A)  $( - \infty , - \sqrt { 3 } ] , [ \sqrt { 3 } , \infty )$ 
B)  $( - \infty , \sqrt { 3 } ] , [ \sqrt { 3 } , \infty )$ 
C)  $[ - \sqrt { 3 } , 0 ] , [ \sqrt { 3 } , \infty )$ 
D)  $[ - \sqrt { 3 } , \sqrt { 3 } ]$ 
E)  $( - \infty , - \sqrt { 3 } ) , ( 0 , \sqrt { 3 } )$ 
A)  $( - \infty , - \sqrt { 3 } ] , [ \sqrt { 3 } , \infty )$ 
B)  $( - \infty , \sqrt { 3 } ] , [ \sqrt { 3 } , \infty )$ 
C)  $[ - \sqrt { 3 } , 0 ] , [ \sqrt { 3 } , \infty )$ 
D)  $[ - \sqrt { 3 } , \sqrt { 3 } ]$ 
E)  $( - \infty , - \sqrt { 3 } ) , ( 0 , \sqrt { 3 } )$

Question 15

Determine the zeros (if any) of the rational function $g ( x ) = 5 + \frac { 4 } { x ^ { 2 } + 5 }$ .

Accepted Answer

A)  $x = - \sqrt { 5 } , x = \sqrt { 5 }$ 
B) x = -4 
C)  $x = - \frac { 4 } { 5 } , x = \frac { 4 } { 5 }$ 
D) x = -5, x = 5 
E) no zeros 
A)  $x = - \sqrt { 5 } , x = \sqrt { 5 }$ 
B) x = -4 
C)  $x = - \frac { 4 } { 5 } , x = \frac { 4 } { 5 }$ 
D) x = -5, x = 5 
E) no zeros

Question 16

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 4 }$ .

Accepted Answer

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

Question 17

From the graph of the quadratic function $f ( x ) = ( x + 6 ) ^ { 2 } - 1$ , determine the equation of the axis of symmetry.

Accepted Answer

A)  $x = - 6$ 
B)  $x = - 1$ 
C)  $x = - \frac { 1 } { 6 }$ 
D)  $x = 1$ 
E)  $x = 6$ 
A)  $x = - 6$ 
B)  $x = - 1$ 
C)  $x = - \frac { 1 } { 6 }$ 
D)  $x = 1$ 
E)  $x = 6$

Question 18

Write the quadratic function $f ( x ) = - x ^ { 2 } + 8 x - 8$ in standard form.

Accepted Answer

A)  $f ( x ) = ( x - 8 ) ^ { 2 } - 4$ 
B)  $f ( x ) = ( x - 4 ) ^ { 2 } - 8$ 
C)  $f ( x ) = - ( x + 4 ) ^ { 2 } + 8$ 
D)  $f ( x ) = - ( x + 8 ) ^ { 2 } - 4$ 
E)  $f ( x ) = - ( x - 4 ) ^ { 2 } + 8$ 
A)  $f ( x ) = ( x - 8 ) ^ { 2 } - 4$ 
B)  $f ( x ) = ( x - 4 ) ^ { 2 } - 8$ 
C)  $f ( x ) = - ( x + 4 ) ^ { 2 } + 8$ 
D)  $f ( x ) = - ( x + 8 ) ^ { 2 } - 4$ 
E)  $f ( x ) = - ( x - 4 ) ^ { 2 } + 8$

Question 19

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x ^ { 2 } + 10 x + 24 } { x ^ { 3 } + 6 x ^ { 2 } - x - 6 }$ .

Accepted Answer

A) horizontal: y = 1; vertical: x = -6 
B) horizontal: y = 0; vertical: x = 1 and x = -6 
C) horizontal: y = 0; vertical: x = -1 and x = 1 
D) horizontal: none; vertical: none 
E) horizontal: y = 0; vertical: x = -6 and x = -4 
A) horizontal: y = 1; vertical: x = -6 
B) horizontal: y = 0; vertical: x = 1 and x = -6 
C) horizontal: y = 0; vertical: x = -1 and x = 1 
D) horizontal: none; vertical: none 
E) horizontal: y = 0; vertical: x = -6 and x = -4

Question 20

Select the graph of the quadratic function $f ( x ) = x ^ { 2 } + 2 x + 2$ .Identify the axis of symmetry.

Accepted Answer

A)    Axis of symmetry: x = -1 
B)     Axis of symmetry: x = -1 
C)    Axis of symmetry: x = -1 
D)     Axis of symmetry: x = -1 
E)    Axis of symmetry: x = -1 
A)    Axis of symmetry: x = -1 
B)     Axis of symmetry: x = -1 
C)    Axis of symmetry: x = -1 
D)     Axis of symmetry: x = -1 
E)    Axis of symmetry: x = -1

Do the operation and express the answer in a + bi form. $( 5 + \sqrt { - 16 } ) ( 4 - \sqrt { - 4 } )$

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } > 2 x + 48$

A small theater has a seating capacity of 2000.When the ticket price is $20, attendance is 1500.For each $1 decrease in price, attendance increases by 125.Write the revenue R of the theater as a function of ticket price x.

Solve the inequality and graph the solution on the real number line. $\frac { 3 x - 5 } { x - 5 } \geq 0$

If x = $\frac { 2 } { 7 }$ is a root of $49 x ^ { 3 } - 126 x ^ { 2 } + 60 x - 8 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Which of the following is the graph of the given equation? $f ( x ) = \frac { 2 - x } { x + 3 }$

Find the values of x and y. x + 59i = y - yi x = y =

Solve the inequality $36 x - x ^ { 3 } < 0$ and write the solution set in interval notation.

Use synthetic division to express $P ( x ) = 3 x ^ { 3 } - 10 x ^ { 2 } - 23 x - 35$ in the form (divisor)(quotient) + remainder for the divisor x - 5.

The growth of a red oak tree is approximated by the function $G = - 0.003 t ^ { 3 } + 0.137 t ^ { 2 } + 0.458 t - 0.839$ Where G is the height of the tree (in feet) and t $( 2 \leq t \leq 34 )$ is its age (in years). Select the correct graph of the function.

Use long division to divide. $\left( x ^ { 4 } + 7 x ^ { 3 } + 10 x ^ { 2 } - x - 2 \right) \div ( x + 2 )$

Use the Remainder Theorem and synthetic division to find the function value. $g ( x ) = 3 x ^ { 6 } + 4 x ^ { 4 } - 6 x ^ { 2 } + 4 , \quad g ( 0 )$

Given $f ( x ) = \frac { x ^ { 2 } + 49 } { x + 7 } , g ( x ) = x - 7$ .Determine the domains of f(x) and g(x).

Find the domain of x in the expression $\sqrt [ 4 ] { x ^ { 3 } - 3 x }$ .

Determine the zeros (if any) of the rational function $g ( x ) = 5 + \frac { 4 } { x ^ { 2 } + 5 }$ .

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 4 }$ .

From the graph of the quadratic function $f ( x ) = ( x + 6 ) ^ { 2 } - 1$ , determine the equation of the axis of symmetry.

Write the quadratic function $f ( x ) = - x ^ { 2 } + 8 x - 8$ in standard form.

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x ^ { 2 } + 10 x + 24 } { x ^ { 3 } + 6 x ^ { 2 } - x - 6 }$ .

Select the graph of the quadratic function $f ( x ) = x ^ { 2 } + 2 x + 2$ .Identify the axis of symmetry.

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

Do the operation and express the answer in a + bi form. (5+−16)(4−−4)( 5 + \sqrt { - 16 } ) ( 4 - \sqrt { - 4 } )(5+−16​)(4−−4​)

Solve the inequality and graph the solution on the real number line. x2>2x+48x ^ { 2 } > 2 x + 48x2>2x+48

A small theater has a seating capacity of 2000.When the ticket price is $20, attendance is 1500.For each $1 decrease in price, attendance increases by 125.Write the revenue R of the theater as a function of ticket price x.

Solve the inequality and graph the solution on the real number line. 3x−5x−5≥0\frac { 3 x - 5 } { x - 5 } \geq 0x−53x−5​≥0

If x = 27\frac { 2 } { 7 }72​ is a root of 49x3−126x2+60x−8=049 x ^ { 3 } - 126 x ^ { 2 } + 60 x - 8 = 049x3−126x2+60x−8=0 , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Which of the following is the graph of the given equation? f(x)=2−xx+3f ( x ) = \frac { 2 - x } { x + 3 }f(x)=x+32−x​

Find the values of x and y. ​ x + 59i = y - yi ​ x = __________ ​ y = __________

Solve the inequality 36x−x3<036 x - x ^ { 3 } < 036x−x3<0 and write the solution set in interval notation.

Use synthetic division to express P(x)=3x3−10x2−23x−35P ( x ) = 3 x ^ { 3 } - 10 x ^ { 2 } - 23 x - 35P(x)=3x3−10x2−23x−35 in the form (divisor)(quotient) + remainder for the divisor x - 5.

Use long division to divide. (x4+7x3+10x2−x−2)÷(x+2)\left( x ^ { 4 } + 7 x ^ { 3 } + 10 x ^ { 2 } - x - 2 \right) \div ( x + 2 )(x4+7x3+10x2−x−2)÷(x+2)

Use the Remainder Theorem and synthetic division to find the function value. g(x)=3x6+4x4−6x2+4,g(0)g ( x ) = 3 x ^ { 6 } + 4 x ^ { 4 } - 6 x ^ { 2 } + 4 , \quad g ( 0 )g(x)=3x6+4x4−6x2+4,g(0)

Given f(x)=x2+49x+7,g(x)=x−7f ( x ) = \frac { x ^ { 2 } + 49 } { x + 7 } , g ( x ) = x - 7f(x)=x+7x2+49​,g(x)=x−7 .Determine the domains of f(x) and g(x).

Find the domain of x in the expression x3−3x4\sqrt [ 4 ] { x ^ { 3 } - 3 x }4x3−3x​ .

Determine the zeros (if any) of the rational function g(x)=5+4x2+5g ( x ) = 5 + \frac { 4 } { x ^ { 2 } + 5 }g(x)=5+x2+54​ .

Determine the equations of any horizontal and vertical asymptotes of f(x)=x2x2+4f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 4 }f(x)=x2+4x2​ .

From the graph of the quadratic function f(x)=(x+6)2−1f ( x ) = ( x + 6 ) ^ { 2 } - 1f(x)=(x+6)2−1 , determine the equation of the axis of symmetry.

Write the quadratic function f(x)=−x2+8x−8f ( x ) = - x ^ { 2 } + 8 x - 8f(x)=−x2+8x−8 in standard form.

Determine the equations of any horizontal and vertical asymptotes of f(x)=x2+10x+24x3+6x2−x−6f ( x ) = \frac { x ^ { 2 } + 10 x + 24 } { x ^ { 3 } + 6 x ^ { 2 } - x - 6 }f(x)=x3+6x2−x−6x2+10x+24​ .

Select the graph of the quadratic function f(x)=x2+2x+2f ( x ) = x ^ { 2 } + 2 x + 2f(x)=x2+2x+2 .Identify the axis of symmetry.

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

Do the operation and express the answer in a + bi form. $( 5 + \sqrt { - 16 } ) ( 4 - \sqrt { - 4 } )$

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } > 2 x + 48$

Solve the inequality and graph the solution on the real number line. $\frac { 3 x - 5 } { x - 5 } \geq 0$

If x = $\frac { 2 } { 7 }$ is a root of $49 x ^ { 3 } - 126 x ^ { 2 } + 60 x - 8 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Which of the following is the graph of the given equation? $f ( x ) = \frac { 2 - x } { x + 3 }$

Find the values of x and y. x + 59i = y - yi x = y =

Solve the inequality $36 x - x ^ { 3 } < 0$ and write the solution set in interval notation.

Use synthetic division to express $P ( x ) = 3 x ^ { 3 } - 10 x ^ { 2 } - 23 x - 35$ in the form (divisor)(quotient) + remainder for the divisor x - 5.

Use long division to divide. $\left( x ^ { 4 } + 7 x ^ { 3 } + 10 x ^ { 2 } - x - 2 \right) \div ( x + 2 )$

Use the Remainder Theorem and synthetic division to find the function value. $g ( x ) = 3 x ^ { 6 } + 4 x ^ { 4 } - 6 x ^ { 2 } + 4 , \quad g ( 0 )$

Given $f ( x ) = \frac { x ^ { 2 } + 49 } { x + 7 } , g ( x ) = x - 7$ .Determine the domains of f(x) and g(x).

Find the domain of x in the expression $\sqrt [ 4 ] { x ^ { 3 } - 3 x }$ .

Determine the zeros (if any) of the rational function $g ( x ) = 5 + \frac { 4 } { x ^ { 2 } + 5 }$ .

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 4 }$ .

From the graph of the quadratic function $f ( x ) = ( x + 6 ) ^ { 2 } - 1$ , determine the equation of the axis of symmetry.

Write the quadratic function $f ( x ) = - x ^ { 2 } + 8 x - 8$ in standard form.

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x ^ { 2 } + 10 x + 24 } { x ^ { 3 } + 6 x ^ { 2 } - x - 6 }$ .

Select the graph of the quadratic function $f ( x ) = x ^ { 2 } + 2 x + 2$ .Identify the axis of symmetry.