Question 1

Solve the inequality and graph the solution on the real number line. 
 $\frac { 2 } { x + 4 } > \frac { 1 } { x - 2 }$

Accepted Answer

A)  $( - 4,2 ) \cup ( 8 , \infty )$   
B)  $( - 4,2 ) \cap ( 8 , \infty )$   
C)  $( - 4 , - 2 ) \cup ( 8 , \infty )$   
D)  $( - 4,2 ) \cap ( - 8 , \infty )$   
E)  $( 4,2 ) \cup ( 8 , \infty )$   
A)  $( - 4,2 ) \cup ( 8 , \infty )$   
B)  $( - 4,2 ) \cap ( 8 , \infty )$   
C)  $( - 4 , - 2 ) \cup ( 8 , \infty )$   
D)  $( - 4,2 ) \cap ( - 8 , \infty )$   
E)  $( 4,2 ) \cup ( 8 , \infty )$

Question 2

Find all the zeros of the function and write the polynomial as a product of linear factors. ​
X2 + 49
​

Accepted Answer

A) 7i; (x + 7i)(x - 7i) 
B) -7i; (x + 7i)(x - 7i) 
C) ±7i; (x + 7)(x - 7) 
D) -7i; (x + 7)(x - 7) 
E) ±7i; (x + 7i)(x - 7i) 
A) 7i; (x + 7i)(x - 7i) 
B) -7i; (x + 7i)(x - 7i) 
C) ±7i; (x + 7)(x - 7) 
D) -7i; (x + 7)(x - 7) 
E) ±7i; (x + 7i)(x - 7i)

Question 3

Use the given zero to find all the zeros of the function.  
Function Zero
7x3 + 8x2 + 175x + 200 5i

Accepted Answer

A) ±5i, $\frac { 8 } { 7 }$ 
B) ±5i, $- \frac { 8 } { 7 }$ 
C) ±5i, -8 
D) ±5i, $- \frac { 7 } { 8 }$ 
E) ±5i, $\pm \frac { 8 } { 7 } i$ 
A) ±5i, $\frac { 8 } { 7 }$ 
B) ±5i, $- \frac { 8 } { 7 }$ 
C) ±5i, -8 
D) ±5i, $- \frac { 7 } { 8 }$ 
E) ±5i, $\pm \frac { 8 } { 7 } i$

Question 4

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + x - 12 }$ .

Accepted Answer

A) horizontal: y = 4; vertical: x = 0 
B) horizontal: y = 1; vertical: x = -4 
C) horizontal: y = 1; vertical: x = 3 and x = -4 
D) horizontal: y = -3; vertical: x = -4 
E) horizontal: y = 0; vertical: none 
A) horizontal: y = 4; vertical: x = 0 
B) horizontal: y = 1; vertical: x = -4 
C) horizontal: y = 1; vertical: x = 3 and x = -4 
D) horizontal: y = -3; vertical: x = -4 
E) horizontal: y = 0; vertical: none

Question 5

Solve the equation and write complex solutions in standard form. 
 $x ^ { 2 } + 10 x + 29 = 0$

Accepted Answer

A)  $x = 10 - 2 i , 10 + 2 i$ 
B)   $x = - 2 - 5 i , - 2 + 5 i$ 
C)   $x = - 5 + 4 i , - 5 - 4 i$ 
D)   $x = - 5 - 2 i , - 5 + 2 i$ 
E)   $x = - 2 + 25 i , - 2 - 25 i$ 
A)  $x = 10 - 2 i , 10 + 2 i$ 
B)   $x = - 2 - 5 i , - 2 + 5 i$ 
C)   $x = - 5 + 4 i , - 5 - 4 i$ 
D)   $x = - 5 - 2 i , - 5 + 2 i$ 
E)   $x = - 2 + 25 i , - 2 - 25 i$

Question 6

Determine the value that the function f approaches as the magnitude of x increases. 
$f ( x ) = \frac { 8 x - 1 } { x ^ { 2 } + 2 }$

Accepted Answer

A) 0 
B)  $- \frac { 1 } { 2 }$ 
C) -1 
D) 8 
E)  $- \frac { 1 } { 5 }$ 
A) 0 
B)  $- \frac { 1 } { 2 }$ 
C) -1 
D) 8 
E)  $- \frac { 1 } { 5 }$

Question 7

Find the domain of x in the expression. 
 $\sqrt { 25 - x ^ { 2 } }$

Accepted Answer

A)  $( - 25,25 )$ 
B)  $[ - 25,25 ]$ 
C)  $( - 5,5 )$ 
D)  $[ - 5,25 )$ 
E)  $[ - 5,5 ]$ 
A)  $( - 25,25 )$ 
B)  $[ - 25,25 ]$ 
C)  $( - 5,5 )$ 
D)  $[ - 5,25 )$ 
E)  $[ - 5,5 ]$

Question 8

Write the quadratic function $f ( x ) = x ^ { 2 } + 2 x + 5$ in standard form.

Accepted Answer

A)  $f ( x ) = - ( x + 1 ) ^ { 2 } - 4$ 
B)  $f ( x ) = ( x - 4 ) ^ { 2 } - 1$ 
C)  $f ( x ) = - ( x - 1 ) ^ { 2 } - 4$ 
D)  $f ( x ) = ( x + 1 ) ^ { 2 } + 4$ 
E)  $f ( x ) = - ( x - 4 ) ^ { 2 } + 1$ 
A)  $f ( x ) = - ( x + 1 ) ^ { 2 } - 4$ 
B)  $f ( x ) = ( x - 4 ) ^ { 2 } - 1$ 
C)  $f ( x ) = - ( x - 1 ) ^ { 2 } - 4$ 
D)  $f ( x ) = ( x + 1 ) ^ { 2 } + 4$ 
E)  $f ( x ) = - ( x - 4 ) ^ { 2 } + 1$

Question 9

Find the domain of x in the following expression. $\sqrt [ 3 ] { x ^ { 4 } - 625 }$

Accepted Answer

A)  $[ - 5,5 ]$ 
B)  $( - \infty , 5 ) \cup ( 5 , \infty )$ 
C)  $[ 5 , \infty )$ 
D)  $( 5 , \infty )$ 
E) all real numbers 
A)  $[ - 5,5 ]$ 
B)  $( - \infty , 5 ) \cup ( 5 , \infty )$ 
C)  $[ 5 , \infty )$ 
D)  $( 5 , \infty )$ 
E) all real numbers

Question 10

An open box is to be made from a square piece of material, 38 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure)      
Where $$a = 38 - 2 x$$ .
Determine the domain of the following function, V(x) represents the volume of the box .
  $V ( x ) = x ( 38 - 2 x ) ^ { 2 }$

Accepted Answer

A) Domain: $0 < x \leq 19$ 
B) Domain: $0 \leq x \leq 38$ 
C) Domain: $0 < x < 38$ 
D) Domain: $0 \leq x \leq 19$ 
E) Domain: $0 < x < 19$ 
A) Domain: $0 < x \leq 19$ 
B) Domain: $0 \leq x \leq 38$ 
C) Domain: $0 < x < 38$ 
D) Domain: $0 \leq x \leq 19$ 
E) Domain: $0 < x < 19$

Question 11

Find the values of b such that the function $f ( x ) = - x ^ { 2 } + b x - 16$ has the given maximum value 65.

Accepted Answer

A) ±18 
B) ±22 
C) ±24 
D) ±20 
E) ±26 
A) ±18 
B) ±22 
C) ±24 
D) ±20 
E) ±26

Question 12

Use synthetic division to divide. $\left( 12 + 5 x ^ { 3 } - 11 x - 18 x ^ { 2 } \right) \div ( x - 4 )$

Accepted Answer

A)  $5 x ^ { 2 } + 2 x - 3$ 
B)   $5 x ^ { 2 } - 7 x + 12$ 
C)  $5 x ^ { 2 } + 2 x + 5$ 
D)  $5 x ^ { 2 } - 23 x - 15$ 
E)  $5 x ^ { 2 } + x - 4$ 
A)  $5 x ^ { 2 } + 2 x - 3$ 
B)   $5 x ^ { 2 } - 7 x + 12$ 
C)  $5 x ^ { 2 } + 2 x + 5$ 
D)  $5 x ^ { 2 } - 23 x - 15$ 
E)  $5 x ^ { 2 } + x - 4$

Question 13

Find all the rational zeros of the function. ​
X3 + 18x2 + 105x + 200
​

Accepted Answer

A) -8, 5 
B) 5, 8 
C) -8, -5 
D) -8, -5, 5 
E) -5, 8 
A) -8, 5 
B) 5, 8 
C) -8, -5 
D) -8, -5, 5 
E) -5, 8

Question 14

Solve the inequality and graph the solution on the real number line. 
 $\frac { x ^ { 2 } + 4 x } { x ^ { 2 } - 25 } \leq 0$

Accepted Answer

A)  $( - 5 , - 4 ] \cup [ 0,5 )$   
B)  $( - 5,4 ] \cup [ 0 , - 5 )$   
C)  $( - 5,4 ] \cup [ 0,5 )$   
D)  $( 5 , - 4 ] \cup [ 0,5 )$   
E)  $( 5,4 ] \cup [ 0,5 )$   
A)  $( - 5 , - 4 ] \cup [ 0,5 )$   
B)  $( - 5,4 ] \cup [ 0 , - 5 )$   
C)  $( - 5,4 ] \cup [ 0,5 )$   
D)  $( 5 , - 4 ] \cup [ 0,5 )$   
E)  $( 5,4 ] \cup [ 0,5 )$

Question 15

A rectangular playing field with a perimeter of 98 meters is to have an area of at least 444 square meters.Within what bounds must the length of the rectangle lie?

Accepted Answer

A)  $444 m \leq L \leq 13 m$ 
B)  $37 m \leq L \leq 98 m$ 
C)  $12 m \leq L \leq 37 m$ 
D)  $39 m \leq L \leq 14 m$ 
E)  $444 m < L < 13 m$ 
A)  $444 m \leq L \leq 13 m$ 
B)  $37 m \leq L \leq 98 m$ 
C)  $12 m \leq L \leq 37 m$ 
D)  $39 m \leq L \leq 14 m$ 
E)  $444 m < L < 13 m$

Question 16

Use synthetic division to divide. $\frac { - 4 x ^ { 3 } + 23 x ^ { 2 } - 31 x + 12 } { 4 x - 3 }$

Accepted Answer

A)  $4 x ^ { 2 } + 12 x + 16$ 
B)  $x ^ { 2 } + 4 x - 4$ 
C)  $- 16 x ^ { 2 } + 12 x + 16$ 
D)  $- 4 x ^ { 2 } - 12 x + 16$ 
E)  $- x ^ { 2 } + 5 x - 4$ 
A)  $4 x ^ { 2 } + 12 x + 16$ 
B)  $x ^ { 2 } + 4 x - 4$ 
C)  $- 16 x ^ { 2 } + 12 x + 16$ 
D)  $- 4 x ^ { 2 } - 12 x + 16$ 
E)  $- x ^ { 2 } + 5 x - 4$

Question 17

Use synthetic division to divide. 
$\left( 3 x ^ { 3 } - 23 x ^ { 2 } + 21 x - 49 \right) \div ( x - 7 )$

Accepted Answer

A)  $2 x ^ { 2 } - 3 x - 7 , x \neq 7$ 
B)  $2 x ^ { 2 } - 3 x + 7 , x \neq 7$ 
C)  $3 x ^ { 2 } - 2 x + 7 , x \neq 7$ 
D)  $3 x ^ { 2 } - 2 x - 7 , x \neq 7$ 
E)  $3 x ^ { 2 } + 2 x + 7 , x \neq 7$ 
A)  $2 x ^ { 2 } - 3 x - 7 , x \neq 7$ 
B)  $2 x ^ { 2 } - 3 x + 7 , x \neq 7$ 
C)  $3 x ^ { 2 } - 2 x + 7 , x \neq 7$ 
D)  $3 x ^ { 2 } - 2 x - 7 , x \neq 7$ 
E)  $3 x ^ { 2 } + 2 x + 7 , x \neq 7$

Question 18

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x - 5 } { x ^ { 2 } - 25 }$ .

Accepted Answer

A) horizontal: y = 0; vertical: x = -5 
B) horizontal: y = -5; vertical: x = 0 
C) horizontal: y = 5; vertical: x = -5 
D) horizontal: y = 0; vertical: x = 5 
E) horizontal: y = 0; vertical: none 
A) horizontal: y = 0; vertical: x = -5 
B) horizontal: y = -5; vertical: x = 0 
C) horizontal: y = 5; vertical: x = -5 
D) horizontal: y = 0; vertical: x = 5 
E) horizontal: y = 0; vertical: none

Question 19

Find two positive real numbers whose product is a maximum.The sum is 140. ​

Accepted Answer

A) 90, 50 
B) ​100, 40 
C) ​70, ​70 
D) ​80, 60 
E) ​10, 130 
A) 90, 50 
B) ​100, 40 
C) ​70, ​70 
D) ​80, 60 
E) ​10, 130

Question 20

Find all the rational zeros of the function $f ( x ) = x ^ { 5 } - 5 x ^ { 4 } + 11 x ^ { 3 } - 23 x ^ { 2 } + 28 x - 12$ .

Accepted Answer

A)  x = -2, 2, 1, 3 
B)  x = 3, 1 
C)  x = -2, -1, -3 
D)  x = -1, -2 
E) x = -2, 2, -1, 1, -3 
A)  x = -2, 2, 1, 3 
B)  x = 3, 1 
C)  x = -2, -1, -3 
D)  x = -1, -2 
E) x = -2, 2, -1, 1, -3

Solve the inequality and graph the solution on the real number line. $\frac { 2 } { x + 4 } > \frac { 1 } { x - 2 }$

Find all the zeros of the function and write the polynomial as a product of linear factors. X² + 49

Use the given zero to find all the zeros of the function. Function Zero 7x³ + 8x² + 175x + 200 5i

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + x - 12 }$ .

Solve the equation and write complex solutions in standard form. $x ^ { 2 } + 10 x + 29 = 0$

Determine the value that the function f approaches as the magnitude of x increases. $f ( x ) = \frac { 8 x - 1 } { x ^ { 2 } + 2 }$

Find the domain of x in the expression. $\sqrt { 25 - x ^ { 2 } }$

Write the quadratic function $f ( x ) = x ^ { 2 } + 2 x + 5$ in standard form.

Find the domain of x in the following expression. $\sqrt [ 3 ] { x ^ { 4 } - 625 }$

Find the values of b such that the function $f ( x ) = - x ^ { 2 } + b x - 16$ has the given maximum value 65.

Use synthetic division to divide. $\left( 12 + 5 x ^ { 3 } - 11 x - 18 x ^ { 2 } \right) \div ( x - 4 )$

Find all the rational zeros of the function. X³ + 18x² + 105x + 200

Solve the inequality and graph the solution on the real number line. $\frac { x ^ { 2 } + 4 x } { x ^ { 2 } - 25 } \leq 0$

A rectangular playing field with a perimeter of 98 meters is to have an area of at least 444 square meters.Within what bounds must the length of the rectangle lie?

Use synthetic division to divide. $\frac { - 4 x ^ { 3 } + 23 x ^ { 2 } - 31 x + 12 } { 4 x - 3 }$

Use synthetic division to divide. $\left( 3 x ^ { 3 } - 23 x ^ { 2 } + 21 x - 49 \right) \div ( x - 7 )$

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x - 5 } { x ^ { 2 } - 25 }$ .

Find two positive real numbers whose product is a maximum.The sum is 140.

Find all the rational zeros of the function $f ( x ) = x ^ { 5 } - 5 x ^ { 4 } + 11 x ^ { 3 } - 23 x ^ { 2 } + 28 x - 12$ .

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

Solve the inequality and graph the solution on the real number line. 2x+4>1x−2\frac { 2 } { x + 4 } > \frac { 1 } { x - 2 }x+42​>x−21​

Find all the zeros of the function and write the polynomial as a product of linear factors. ​ X2 + 49 ​

Use the given zero to find all the zeros of the function. Function Zero 7x3 + 8x2 + 175x + 200 5i

Determine the equations of any horizontal and vertical asymptotes of f(x)=x2−9x2+x−12f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + x - 12 }f(x)=x2+x−12x2−9​ .

Solve the equation and write complex solutions in standard form. x2+10x+29=0x ^ { 2 } + 10 x + 29 = 0x2+10x+29=0

Determine the value that the function f approaches as the magnitude of x increases. f(x)=8x−1x2+2f ( x ) = \frac { 8 x - 1 } { x ^ { 2 } + 2 }f(x)=x2+28x−1​

Find the domain of x in the expression. 25−x2\sqrt { 25 - x ^ { 2 } }25−x2​

Write the quadratic function f(x)=x2+2x+5f ( x ) = x ^ { 2 } + 2 x + 5f(x)=x2+2x+5 in standard form.

Find the domain of x in the following expression. x4−6253\sqrt [ 3 ] { x ^ { 4 } - 625 }3x4−625​

Find the values of b such that the function f(x)=−x2+bx−16f ( x ) = - x ^ { 2 } + b x - 16f(x)=−x2+bx−16 has the given maximum value 65.

Use synthetic division to divide. (12+5x3−11x−18x2)÷(x−4)\left( 12 + 5 x ^ { 3 } - 11 x - 18 x ^ { 2 } \right) \div ( x - 4 )(12+5x3−11x−18x2)÷(x−4)

Find all the rational zeros of the function. ​ X3 + 18x2 + 105x + 200 ​

Solve the inequality and graph the solution on the real number line. x2+4xx2−25≤0\frac { x ^ { 2 } + 4 x } { x ^ { 2 } - 25 } \leq 0x2−25x2+4x​≤0

A rectangular playing field with a perimeter of 98 meters is to have an area of at least 444 square meters.Within what bounds must the length of the rectangle lie?

Use synthetic division to divide. −4x3+23x2−31x+124x−3\frac { - 4 x ^ { 3 } + 23 x ^ { 2 } - 31 x + 12 } { 4 x - 3 }4x−3−4x3+23x2−31x+12​

Use synthetic division to divide. (3x3−23x2+21x−49)÷(x−7)\left( 3 x ^ { 3 } - 23 x ^ { 2 } + 21 x - 49 \right) \div ( x - 7 )(3x3−23x2+21x−49)÷(x−7)

Determine the equations of any horizontal and vertical asymptotes of f(x)=x−5x2−25f ( x ) = \frac { x - 5 } { x ^ { 2 } - 25 }f(x)=x2−25x−5​ .

Find two positive real numbers whose product is a maximum.The sum is 140. ​

Find all the rational zeros of the function f(x)=x5−5x4+11x3−23x2+28x−12f ( x ) = x ^ { 5 } - 5 x ^ { 4 } + 11 x ^ { 3 } - 23 x ^ { 2 } + 28 x - 12f(x)=x5−5x4+11x3−23x2+28x−12 .

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

Solve the inequality and graph the solution on the real number line. $\frac { 2 } { x + 4 } > \frac { 1 } { x - 2 }$

Find all the zeros of the function and write the polynomial as a product of linear factors. X² + 49

Use the given zero to find all the zeros of the function. Function Zero 7x³ + 8x² + 175x + 200 5i

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + x - 12 }$ .

Solve the equation and write complex solutions in standard form. $x ^ { 2 } + 10 x + 29 = 0$

Determine the value that the function f approaches as the magnitude of x increases. $f ( x ) = \frac { 8 x - 1 } { x ^ { 2 } + 2 }$

Find the domain of x in the expression. $\sqrt { 25 - x ^ { 2 } }$

Write the quadratic function $f ( x ) = x ^ { 2 } + 2 x + 5$ in standard form.

Find the domain of x in the following expression. $\sqrt [ 3 ] { x ^ { 4 } - 625 }$

Find the values of b such that the function $f ( x ) = - x ^ { 2 } + b x - 16$ has the given maximum value 65.

Use synthetic division to divide. $\left( 12 + 5 x ^ { 3 } - 11 x - 18 x ^ { 2 } \right) \div ( x - 4 )$

Find all the rational zeros of the function. X³ + 18x² + 105x + 200

Solve the inequality and graph the solution on the real number line. $\frac { x ^ { 2 } + 4 x } { x ^ { 2 } - 25 } \leq 0$

Use synthetic division to divide. $\frac { - 4 x ^ { 3 } + 23 x ^ { 2 } - 31 x + 12 } { 4 x - 3 }$

Use synthetic division to divide. $\left( 3 x ^ { 3 } - 23 x ^ { 2 } + 21 x - 49 \right) \div ( x - 7 )$

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x - 5 } { x ^ { 2 } - 25 }$ .

Find two positive real numbers whose product is a maximum.The sum is 140.

Find all the rational zeros of the function $f ( x ) = x ^ { 5 } - 5 x ^ { 4 } + 11 x ^ { 3 } - 23 x ^ { 2 } + 28 x - 12$ .