Question 1

Find the domain of the function and identify any vertical and horizontal asymptotes. 
 $f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } - 49 }$

Accepted Answer

A) Domain: all real numbers x except x = 0Vertical asymptote: x = ±7Horizontal asymptote: No horizontal asymptote 
B) Domain: all real numbers x except x = ±7Vertical asymptote: x = ±7Horizontal asymptote: No horizontal asymptote 
C) Domain: all real numbers x except x = 7Vertical asymptote: x = 7Horizontal asymptote: y = 7 
D) Domain: all real numbers xVertical asymptote: x = -7Horizontal asymptote: y = 0 
E) Domain: all real numbers x except x = 0Vertical asymptote: x = 0Horizontal asymptote: y = -49 
A) Domain: all real numbers x except x = 0Vertical asymptote: x = ±7Horizontal asymptote: No horizontal asymptote 
B) Domain: all real numbers x except x = ±7Vertical asymptote: x = ±7Horizontal asymptote: No horizontal asymptote 
C) Domain: all real numbers x except x = 7Vertical asymptote: x = 7Horizontal asymptote: y = 7 
D) Domain: all real numbers xVertical asymptote: x = -7Horizontal asymptote: y = 0 
E) Domain: all real numbers x except x = 0Vertical asymptote: x = 0Horizontal asymptote: y = -49

Question 2

Simplify the complex number and write it in standard form.

$\frac { 14 } { i ^ { 3 } }$

Accepted Answer

A)  14i3 
B)  -14i3 
C)  14 
D)  -14i 
E)  14i 
A)  14i3 
B)  -14i3 
C)  14 
D)  -14i 
E)  14i

Question 3

Use the Remainder Theorem and synthetic division to find each function value.Verify your answers using another method.
  $h ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 6 x + 5 , h ( - 10 )$

Accepted Answer

A) -1,237 
B) -1,231 
C) -1,234 
D) -1,235 
E) -1,233 
A) -1,237 
B) -1,231 
C) -1,234 
D) -1,235 
E) -1,233

Question 4

Sketch the graph of the function by finding the zeros of the polynomial, 
 $f ( x ) = 2 x ^ { 3 } - 10 x ^ { 2 } + 12 x$

Accepted Answer

A)  0, 2, 3   
B)  0, 2, -3   
C)  0, -2, 3   
D)  0, 2, 3   
E)  0, -2, -3   
A)  0, 2, 3   
B)  0, 2, -3   
C)  0, -2, 3   
D)  0, 2, 3   
E)  0, -2, -3

Question 5

Simplify the complex number and write it in standard form. 
 $- 5 i ^ { 3 } + i ^ { 2 }$

Accepted Answer

A)   $1 + 5 i$ 
B)   $- 1 - 5 i$ 
C)   $- 5 i$ 
D)   $1 - 5 i$ 
E)   $- 1 + 5 i$ 
A)   $1 + 5 i$ 
B)   $- 1 - 5 i$ 
C)   $- 5 i$ 
D)   $1 - 5 i$ 
E)   $- 1 + 5 i$

Question 6

Use synthetic division to perform the division.  $\frac { 3 x ^ { 4 } - 7 x ^ { 3 } - 16 x + 5 } { x - 3 }$

Accepted Answer

A)  $x ^ { 3 } + x ^ { 2 } + 3 x + 2 - \frac { 11 } { x - 3 }$ 
B)  $3 x ^ { 3 } + 2 x ^ { 2 } + 6 x + 2 + \frac { 11 } { x - 3 }$ 
C)  $3 x ^ { 3 } - 2 x ^ { 2 } + 6 x - 2 + \frac { 11 } { x - 3 }$ 
D)  $3 x ^ { 3 } + 2 x ^ { 2 } + 6 x + 2 + 11$ 
E) none of these 
A)  $x ^ { 3 } + x ^ { 2 } + 3 x + 2 - \frac { 11 } { x - 3 }$ 
B)  $3 x ^ { 3 } + 2 x ^ { 2 } + 6 x + 2 + \frac { 11 } { x - 3 }$ 
C)  $3 x ^ { 3 } - 2 x ^ { 2 } + 6 x - 2 + \frac { 11 } { x - 3 }$ 
D)  $3 x ^ { 3 } + 2 x ^ { 2 } + 6 x + 2 + 11$ 
E) none of these

Question 7

Find two positive real numbers whose product is a maximum and whose sum is 160.

Accepted Answer

A)  $89,71$ 
B)  $85,75$ 
C)  $80,80$ 
D)  $78,82$ 
E)  $92,68$ 
A)  $89,71$ 
B)  $85,75$ 
C)  $80,80$ 
D)  $78,82$ 
E)  $92,68$

Question 8

Solve the inequality and graph the solution on the real number line 
 $x ^ { 2 } \leq 9$

Accepted Answer

A)  $( - 3,3 )$   
B)   $[ - 3,3 ]$   
C)  $[ - 3,3 ]$   
D)  $[ 3 , - 3 ]$   
E)  $( - 3,3 )$   
A)  $( - 3,3 )$   
B)   $[ - 3,3 ]$   
C)  $[ - 3,3 ]$   
D)  $[ 3 , - 3 ]$   
E)  $( - 3,3 )$

Question 9

Select the graph of the function and use the zero or root feature to approximate the real zeros of the function. 
 $g ( x ) = \frac { 1 } { 5 } ( x + 1 ) ^ { 2 } ( x - 3 ) ( 2 x - 7 )$

Accepted Answer

A)  Zeros: $- 1,3 , \pm \frac { 7 } { 2 }$   
B)  Zeros: $- 1,3 , - \frac { 7 } { 2 }$   
C)  Zeros: $- 1 , \pm 3 , \frac { 7 } { 2 }$   
D)  Zeros: $- 1 , - 3 , \frac { 7 } { 2 }$   
E)  Zeros: $- 1,3 , \frac { 7 } { 2 }$   
A)  Zeros: $- 1,3 , \pm \frac { 7 } { 2 }$   
B)  Zeros: $- 1,3 , - \frac { 7 } { 2 }$   
C)  Zeros: $- 1 , \pm 3 , \frac { 7 } { 2 }$   
D)  Zeros: $- 1 , - 3 , \frac { 7 } { 2 }$   
E)  Zeros: $- 1,3 , \frac { 7 } { 2 }$

Question 10

Find the value of k such that ​
X - 6 is a factor of x3 - kx2 + 2kx - 24.
​

Accepted Answer

A) ​k = 6 
B) ​k = 10 
C) ​k = 8 
D) ​k = 7 
E) ​k = 9 
A) ​k = 6 
B) ​k = 10 
C) ​k = 8 
D) ​k = 7 
E) ​k = 9

Question 11

Find all zeros of the function f(x) = (x - 4)(x + 3)[x + (4 + 3i)][x - (4 - 3i)].

Accepted Answer

A) x = 4, -3, -4 - 3i, 4 - 3i 
B) x = -4, 3, 4 - 3i, 4 + 3i 
C) x = -4, 3, 4 + 3i, -4 - 3i 
D) x = 4, -3, 4 + 3i, -4 + 3i 
E) x = 4, -3, -4 - 3i, 4 + 3i 
A) x = 4, -3, -4 - 3i, 4 - 3i 
B) x = -4, 3, 4 - 3i, 4 + 3i 
C) x = -4, 3, 4 + 3i, -4 - 3i 
D) x = 4, -3, 4 + 3i, -4 + 3i 
E) x = 4, -3, -4 - 3i, 4 + 3i

Question 12

Select the graph of the function and use the zero or root feature to approximate the real zeros of the function. 
 $f ( x ) = x ^ { 3 } - 4 x$

Accepted Answer

A)  Zeros: $0 , - 2$   
B)  Zeros: $0 , - 2$   
C)  Zeros: $0,2$   
D)  Zeros: $0 , \pm 2$   
E)  Zeros: $0 , \pm 2$   
A)  Zeros: $0 , - 2$   
B)  Zeros: $0 , - 2$   
C)  Zeros: $0,2$   
D)  Zeros: $0 , \pm 2$   
E)  Zeros: $0 , \pm 2$

Question 13

Find the domain of $f ( x ) = \frac { x - 7 } { x ^ { 2 } - 49 }$ .

Accepted Answer

A) all real numbers except x = -7 
B) all real numbers except x = 49 
C) all real numbers except x = 7 
D) all real numbers except x = 7 and x = -7 
E) all real numbers 
A) all real numbers except x = -7 
B) all real numbers except x = 49 
C) all real numbers except x = 7 
D) all real numbers except x = 7 and x = -7 
E) all real numbers

Question 14

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. 
$5 + 3 i$

Accepted Answer

A)   $5 + 3 i , 34$ 
B)   $5 - 3 i , 9$ 
C)   $5 + 3 i , 9$ 
D)   $- 5 - 3 i , 34$ 
E)   $5 - 3 i , 34$ 
A)   $5 + 3 i , 34$ 
B)   $5 - 3 i , 9$ 
C)   $5 + 3 i , 9$ 
D)   $- 5 - 3 i , 34$ 
E)   $5 - 3 i , 34$

Question 15

Find a polynomial with the given zeros.  $0,0,0 , \sqrt { 3 } , - \sqrt { 3 }$

Accepted Answer

A)  $x ^ { 5 } - 3 x ^ { 3 }$ 
B)  $x ^ { 5 } - 6 x ^ { 3 }$ 
C)  $x ^ { 5 } - x ^ { 3 } + 3$ 
D)  $x ^ { 2 } + 3 x + 6$ 
E) none of these 
A)  $x ^ { 5 } - 3 x ^ { 3 }$ 
B)  $x ^ { 5 } - 6 x ^ { 3 }$ 
C)  $x ^ { 5 } - x ^ { 3 } + 3$ 
D)  $x ^ { 2 } + 3 x + 6$ 
E) none of these

Question 16

Write the complex number in standard form. 
$8 + \sqrt { - 25 }$

Accepted Answer

A)   $8 + 25 i$ 
B)   $11 - 8 i$ 
C)   $11 + 8 i$ 
D)   $8 - 5 i$ 
E)   $8 + 5 i$ 
A)   $8 + 25 i$ 
B)   $11 - 8 i$ 
C)   $11 + 8 i$ 
D)   $8 - 5 i$ 
E)   $8 + 5 i$

Question 17

Find the standard form of the quadratic function shown below:

Accepted Answer

A)  $f ( x ) = ( x + 2 ) ^ { 2 } - 3$ 
B)  $f ( x ) =$ $\frac { 1 } { 2 }$ $( x - 2 ) ^ { 2 } + 3$ 
C)  $f ( x ) = -$ $\frac { 2 } { 3 }$ $( x - 1 ) ^ { 2 } + 3$ 
D)  $f ( x ) =$ $\frac { 1 } { 2 }$ $( x + 2 ) ^ { 2 } - 3$ 
E)  $f ( x ) =$ $\frac { 1 } { 4 }$ $( x - 2 ) ^ { 2 } + 3$ 
A)  $f ( x ) = ( x + 2 ) ^ { 2 } - 3$ 
B)  $f ( x ) =$ $\frac { 1 } { 2 }$ $( x - 2 ) ^ { 2 } + 3$ 
C)  $f ( x ) = -$ $\frac { 2 } { 3 }$ $( x - 1 ) ^ { 2 } + 3$ 
D)  $f ( x ) =$ $\frac { 1 } { 2 }$ $( x + 2 ) ^ { 2 } - 3$ 
E)  $f ( x ) =$ $\frac { 1 } { 4 }$ $( x - 2 ) ^ { 2 } + 3$

Question 18

Perform the addition or subtraction and write the result in standard form.   $( 7 + i ) + ( 5 - 5 i )$

Accepted Answer

A) 16  - 8i 
B)  15 - 7i 
C)  12 - 4i 
D)  14 - 6i 
E)  13 - 5i 
A) 16  - 8i 
B)  15 - 7i 
C)  12 - 4i 
D)  14 - 6i 
E)  13 - 5i

Question 19

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. 
$- 1 - \sqrt { 7 } i$

Accepted Answer

A)   $- 1 + \sqrt { 7 } i , 100$ 
B)   $- 1 + \sqrt { 7 } i , 8$ 
C)   $- 1 + \sqrt { 7 } i , - 6$ 
D)   $1 - \sqrt { 7 i } , 100$ 
E)   $1 + \sqrt { 7 } i , 8$ 
A)   $- 1 + \sqrt { 7 } i , 100$ 
B)   $- 1 + \sqrt { 7 } i , 8$ 
C)   $- 1 + \sqrt { 7 } i , - 6$ 
D)   $1 - \sqrt { 7 i } , 100$ 
E)   $1 + \sqrt { 7 } i , 8$

Question 20

Do the operation and express the answer in a + bi form.Do not use parentheses in your answer.
​
(3 - 8i) + (10 + 5i)

Accepted Answer

The answer of Do the operation and express the answer...

Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } - 49 }$

Simplify the complex number and write it in standard form. $\frac { 14 } { i ^ { 3 } }$

Use the Remainder Theorem and synthetic division to find each function value.Verify your answers using another method. $h ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 6 x + 5 , h ( - 10 )$

Sketch the graph of the function by finding the zeros of the polynomial, $f ( x ) = 2 x ^ { 3 } - 10 x ^ { 2 } + 12 x$

Simplify the complex number and write it in standard form. $- 5 i ^ { 3 } + i ^ { 2 }$

Use synthetic division to perform the division. $\frac { 3 x ^ { 4 } - 7 x ^ { 3 } - 16 x + 5 } { x - 3 }$

Find two positive real numbers whose product is a maximum and whose sum is 160.

Solve the inequality and graph the solution on the real number line $x ^ { 2 } \leq 9$

Select the graph of the function and use the zero or root feature to approximate the real zeros of the function. $g ( x ) = \frac { 1 } { 5 } ( x + 1 ) ^ { 2 } ( x - 3 ) ( 2 x - 7 )$

Find the value of k such that X - 6 is a factor of x³ - kx² + 2kx - 24.

Find all zeros of the function f(x) = (x - 4)(x + 3)[x + (4 + 3i)][x - (4 - 3i)].

Select the graph of the function and use the zero or root feature to approximate the real zeros of the function. $f ( x ) = x ^ { 3 } - 4 x$

Find the domain of $f ( x ) = \frac { x - 7 } { x ^ { 2 } - 49 }$ .

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. $5 + 3 i$

Find a polynomial with the given zeros. $0,0,0 , \sqrt { 3 } , - \sqrt { 3 }$

Write the complex number in standard form. $8 + \sqrt { - 25 }$

Find the standard form of the quadratic function shown below:

Perform the addition or subtraction and write the result in standard form. $( 7 + i ) + ( 5 - 5 i )$

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. $- 1 - \sqrt { 7 } i$

Do the operation and express the answer in a + bi form.Do not use parentheses in your answer. (3 - 8i) + (10 + 5i)

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

Find the domain of the function and identify any vertical and horizontal asymptotes. f(x)=x3x2−49f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } - 49 }f(x)=x2−49x3​

Simplify the complex number and write it in standard form. 14i3\frac { 14 } { i ^ { 3 } }i314​

Use the Remainder Theorem and synthetic division to find each function value.Verify your answers using another method. h(x)=x3−3x2−6x+5,h(−10)h ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 6 x + 5 , h ( - 10 )h(x)=x3−3x2−6x+5,h(−10)

Sketch the graph of the function by finding the zeros of the polynomial, f(x)=2x3−10x2+12xf ( x ) = 2 x ^ { 3 } - 10 x ^ { 2 } + 12 xf(x)=2x3−10x2+12x

Simplify the complex number and write it in standard form. −5i3+i2- 5 i ^ { 3 } + i ^ { 2 }−5i3+i2

Use synthetic division to perform the division. 3x4−7x3−16x+5x−3\frac { 3 x ^ { 4 } - 7 x ^ { 3 } - 16 x + 5 } { x - 3 }x−33x4−7x3−16x+5​

Find two positive real numbers whose product is a maximum and whose sum is 160.

Solve the inequality and graph the solution on the real number line x2≤9x ^ { 2 } \leq 9x2≤9

Select the graph of the function and use the zero or root feature to approximate the real zeros of the function. g(x)=15(x+1)2(x−3)(2x−7)g ( x ) = \frac { 1 } { 5 } ( x + 1 ) ^ { 2 } ( x - 3 ) ( 2 x - 7 )g(x)=51​(x+1)2(x−3)(2x−7)

Find the value of k such that ​ X - 6 is a factor of x3 - kx2 + 2kx - 24. ​

Find all zeros of the function f(x) = (x - 4)(x + 3)[x + (4 + 3i)][x - (4 - 3i)].

Select the graph of the function and use the zero or root feature to approximate the real zeros of the function. f(x)=x3−4xf ( x ) = x ^ { 3 } - 4 xf(x)=x3−4x

Find the domain of f(x)=x−7x2−49f ( x ) = \frac { x - 7 } { x ^ { 2 } - 49 }f(x)=x2−49x−7​ .

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. 5+3i5 + 3 i5+3i

Find a polynomial with the given zeros. 0,0,0,3,−30,0,0 , \sqrt { 3 } , - \sqrt { 3 }0,0,0,3​,−3​

Write the complex number in standard form. 8+−258 + \sqrt { - 25 }8+−25​

Find the standard form of the quadratic function shown below:

Perform the addition or subtraction and write the result in standard form. (7+i)+(5−5i)( 7 + i ) + ( 5 - 5 i )(7+i)+(5−5i)

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. −1−7i- 1 - \sqrt { 7 } i−1−7​i

Do the operation and express the answer in a + bi form.Do not use parentheses in your answer. ​ (3 - 8i) + (10 + 5i)

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

Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } - 49 }$

Simplify the complex number and write it in standard form. $\frac { 14 } { i ^ { 3 } }$

Use the Remainder Theorem and synthetic division to find each function value.Verify your answers using another method. $h ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 6 x + 5 , h ( - 10 )$

Sketch the graph of the function by finding the zeros of the polynomial, $f ( x ) = 2 x ^ { 3 } - 10 x ^ { 2 } + 12 x$

Simplify the complex number and write it in standard form. $- 5 i ^ { 3 } + i ^ { 2 }$

Use synthetic division to perform the division. $\frac { 3 x ^ { 4 } - 7 x ^ { 3 } - 16 x + 5 } { x - 3 }$

Solve the inequality and graph the solution on the real number line $x ^ { 2 } \leq 9$

Select the graph of the function and use the zero or root feature to approximate the real zeros of the function. $g ( x ) = \frac { 1 } { 5 } ( x + 1 ) ^ { 2 } ( x - 3 ) ( 2 x - 7 )$

Find the value of k such that X - 6 is a factor of x³ - kx² + 2kx - 24.

Select the graph of the function and use the zero or root feature to approximate the real zeros of the function. $f ( x ) = x ^ { 3 } - 4 x$

Find the domain of $f ( x ) = \frac { x - 7 } { x ^ { 2 } - 49 }$ .

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. $5 + 3 i$

Find a polynomial with the given zeros. $0,0,0 , \sqrt { 3 } , - \sqrt { 3 }$

Write the complex number in standard form. $8 + \sqrt { - 25 }$

Perform the addition or subtraction and write the result in standard form. $( 7 + i ) + ( 5 - 5 i )$

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. $- 1 - \sqrt { 7 } i$

Do the operation and express the answer in a + bi form.Do not use parentheses in your answer. (3 - 8i) + (10 + 5i)