Question 1

Simplify the complex number and write it in standard form. $\frac { 1 } { ( 8 i ) ^ { 3 } }$

Accepted Answer

A)  $\frac { 1 } { 8 } i$ 
B) $- \frac { 1 } { 8 } i$ 
C)  $512 i$ 
D)  $\frac { 1 } { 512 } i$ 
E)  $- \frac { 1 } { 512 } i$ 
A)  $\frac { 1 } { 8 } i$ 
B) $- \frac { 1 } { 8 } i$ 
C)  $512 i$ 
D)  $\frac { 1 } { 512 } i$ 
E)  $- \frac { 1 } { 512 } i$

Question 2

Find all the zeros of the function and write the polynomial as a product of linear fac- tors. 
$y ^ { 4 } - 16$

Accepted Answer

A)  $\pm 2 ( y - 2 ) ( y + 2 )$ 
B)  $\pm 2 , \pm 2 i ; ( y - 2 ) ( y - 2 ) ( y + 2 i ) ( y + 2 i )$ 
C)  $\pm 2 , \pm 2 i ; ( y - 2 ) ( y + 2 ) ( y - 2 i ) ( y + 2 i )$ 
D)  $\pm 2 i ; ( y - 2 i ) ( y + 2 i )$ 
E)  $2,2 i ; ( y + 2 ) ( y + 2 ) ( y - 2 i ) ( y - 2 i )$ 
A)  $\pm 2 ( y - 2 ) ( y + 2 )$ 
B)  $\pm 2 , \pm 2 i ; ( y - 2 ) ( y - 2 ) ( y + 2 i ) ( y + 2 i )$ 
C)  $\pm 2 , \pm 2 i ; ( y - 2 ) ( y + 2 ) ( y - 2 i ) ( y + 2 i )$ 
D)  $\pm 2 i ; ( y - 2 i ) ( y + 2 i )$ 
E)  $2,2 i ; ( y + 2 ) ( y + 2 ) ( y - 2 i ) ( y - 2 i )$

Question 3

Solve the inequality and write the solution set in interval notation. 
$x ^ { 4 } ( x - 3 ) \leq 0$

Accepted Answer

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

Question 4

Select the correct graph of the following function. 
$f ( x ) = \frac { x ^ { 2 } - 49 } { x + 7 }$

Accepted Answer

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

Question 5

Perform the addition or subtraction and write the result in standard form. $( 3 + i ) + ( 4 - 3 i )$

Accepted Answer

A)  $11 - 6 i$ 
B)  $10 - 5 i$ 
C)  $7 - 2 i$ 
D)  $9 - 4 i$ 
E)  $8 - 3 i$ 
A)  $11 - 6 i$ 
B)  $10 - 5 i$ 
C)  $7 - 2 i$ 
D)  $9 - 4 i$ 
E)  $8 - 3 i$

Question 6

Solve the inequality and graph the solution on the real number line $x ^ { 2 } \leq 16$

Accepted Answer

A)  $[ - 4,4 ]$
  
B)  $( - 4,4 )$
  
C)  $( - 4,4 )$
  
D)  $[ 4 , - 4 ]$
  
E)  $[ - 4,4 ]$
  
A)  $[ - 4,4 ]$
  
B)  $( - 4,4 )$
  
C)  $( - 4,4 )$
  
D)  $[ 4 , - 4 ]$
  
E)  $[ - 4,4 ]$

Question 7

The total revenue $\ {R }$ earned per day (in dollars) from a pet-sitting service is given by  $R ( p ) = - 12 p ^ { 2 } + 150 p$           where, $p$ is the price charged per pet (in dollars). Find the revenue when the price per pet is $\$ 9$.

Accepted Answer

A)  $\$ 398$ 
B)  $\$ 388$ 
C)  $\$ 418$ 
D)  $\$ 408$ 
E)  $\$ 378$ 
A)  $\$ 398$ 
B)  $\$ 388$ 
C)  $\$ 418$ 
D)  $\$ 408$ 
E)  $\$ 378$

Question 8

Describe the right-hand and the left-hand behavior of the graph of 
$\ { m ( x ) } = - 3 x ^ { 4 } + 2 x ^ { 3 } + 29$

Accepted Answer

A)  Because the degree is even and the leading coefficient is negative, the graph falls to the left and rises to the right. 
B)  Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right. 
C)  Because the degree is even and the leading coefficient is negative, the graph falls to the left and falls to the right. 
D)  Because the degree is even and the leading coefficient is negative, the graph rises to the left and rises to the right. 
E)  Because the degree is odd and the leading coefficient is negative, the graph rises to the left and rises to the right. 
A)  Because the degree is even and the leading coefficient is negative, the graph falls to the left and rises to the right. 
B)  Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right. 
C)  Because the degree is even and the leading coefficient is negative, the graph falls to the left and falls to the right. 
D)  Because the degree is even and the leading coefficient is negative, the graph rises to the left and rises to the right. 
E)  Because the degree is odd and the leading coefficient is negative, the graph rises to the left and rises to the right.

Question 9

Solve the inequality and write the solution set in interval notation. 
$x ^ { 5 } ( x - 4 ) \leq 0$

Accepted Answer

A)  $( \infty , 4 ]$ 
B)  $( - \infty , - 4 ]$ 
C)  $( \infty , 4 )$ 
D)  $( - 4,4 ]$ 
E)  $( - \infty , 4 ]$ 
A)  $( \infty , 4 ]$ 
B)  $( - \infty , - 4 ]$ 
C)  $( \infty , 4 )$ 
D)  $( - 4,4 ]$ 
E)  $( - \infty , 4 ]$

Question 10

Select the correct graph of the following function. $$f ( x ) = 6 x ^ { 3 } + x ^ { 2 } - 7 x + 4$$

Accepted Answer

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

Question 11

Select the correct graph of the following function. $f ( x ) = \frac { x ^ { 2 } - 25 } { x + 5 }$

Accepted Answer

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

Question 12

Find all the rational zeros of the function $f ( x ) = 2 x ^ { 5 } - 9 x ^ { 4 } + 9 x ^ { 3 } - 3 x ^ { 2 } + 7 x + 6$

Accepted Answer

A)  $x = - \frac { 1 } { 2 } , 3,2$ 
B)  $x = - \frac { 1 } { 2 } , \frac { 3 } { 2 }$ 
C)  $x = - \frac { 2 } { 3 } , - 1,2$ 
D)  $x = \frac { 1 } { 2 } , 3,1$ 
E)  $x = - \frac { 1 } { 2 } , \frac { 3 } { 2 } , 2$ 
A)  $x = - \frac { 1 } { 2 } , 3,2$ 
B)  $x = - \frac { 1 } { 2 } , \frac { 3 } { 2 }$ 
C)  $x = - \frac { 2 } { 3 } , - 1,2$ 
D)  $x = \frac { 1 } { 2 } , 3,1$ 
E)  $x = - \frac { 1 } { 2 } , \frac { 3 } { 2 } , 2$

Question 13

If $x = \sqrt { 7 } \text { is a root of } x ^ { 3 } - 3 x ^ { 2 } - 7 x + 21 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Accepted Answer

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

Question 14

Perform the operation and write the result in standard form. $( 10 - 9 i ) ^ { 2 }$

Accepted Answer

A)  $19 - 180 i$ 
B)  $- 19 - 180 i$ 
C)  $19 + 180 i$ 
D)  $21 - 180 i$ 
E)  $- 19 + 180 i$ 
A)  $19 - 180 i$ 
B)  $- 19 - 180 i$ 
C)  $19 + 180 i$ 
D)  $21 - 180 i$ 
E)  $- 19 + 180 i$

Question 15

Write the complex number in standard form. $\sqrt { - 9 }$

Accepted Answer

A)  $3 i$ 
B)  $- 3 i$ 
C)  $9 i$ 
D)  $4 i$ 
E)  $- 9 i$ 
A)  $3 i$ 
B)  $- 3 i$ 
C)  $9 i$ 
D)  $4 i$ 
E)  $- 9 i$

Question 16

Select the correct graph of the functions f and g in the same viewing window. Zoom out sufficiently far to show that the right-hand and left-hand behaviors of and appear identical.  $f ( x ) = x ^ { 3 } - 5 x + 1 , \quad g ( x ) = x ^ { 3 }$

Accepted Answer

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

Question 17

Solve the inequality and graph the solution on the real number line $x ^ { 2 } \leq 16$

Accepted Answer

A)  $( - 4,4 )$
  
B)  $[ - 4,4 ]$
  
C)  $[ - 4,4 ]$
  
D)  $[ 4 , - 4 ]$
  
E)  $( - 4,4 )$
  
A)  $( - 4,4 )$
  
B)  $[ - 4,4 ]$
  
C)  $[ - 4,4 ]$
  
D)  $[ 4 , - 4 ]$
  
E)  $( - 4,4 )$

Question 18

Find all the zeros of the function and write the polynomial as a product of linear fac- tors. 
$x ^ { 4 } + 29 x ^ { 2 } + 100$

Accepted Answer

A)  $\pm 5 i , \pm 2 ; ( x + 5 i ) ( x - 5 i ) ( x + 2 ) ( x - 2 )$ 
B)  $\pm 5 i , \pm 2 i ; ( x + 5 i ) ( x - 5 i ) ( x + 2 i ) ( x - 2 i )$ 
C)  $- 5 i , - 2 i ; ( x - 5 i ) ( x - 5 i ) ( x - 2 i ) ( x - 2 i )$ 
D)  $5 i , 2 i ; ( x + 5 i ) ( x + 5 i ) ( x + 2 i ) ( x + 2 i )$ 
E)  $\pm 5 , \pm 2 i ; ( x + 5 ) ( x - 5 ) ( x + 2 i ) ( x - 2 i )$ 
A)  $\pm 5 i , \pm 2 ; ( x + 5 i ) ( x - 5 i ) ( x + 2 ) ( x - 2 )$ 
B)  $\pm 5 i , \pm 2 i ; ( x + 5 i ) ( x - 5 i ) ( x + 2 i ) ( x - 2 i )$ 
C)  $- 5 i , - 2 i ; ( x - 5 i ) ( x - 5 i ) ( x - 2 i ) ( x - 2 i )$ 
D)  $5 i , 2 i ; ( x + 5 i ) ( x + 5 i ) ( x + 2 i ) ( x + 2 i )$ 
E)  $\pm 5 , \pm 2 i ; ( x + 5 ) ( x - 5 ) ( x + 2 i ) ( x - 2 i )$

Question 19

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 4 } { x - 5 }$

Accepted Answer

A)  horizontal: $y = 4$; vertical: $x = 5$ 
B)  horizontal: $x = 0$; vertical: $y = 5$ 
C)  horizontal: $y = - 5$; vertical: $x = 0$ 
D)  horizontal: $x = 5$; vertical: $y = - 4$ 
E)  horizontal: $y = 0$; vertical: $x = 5$ 
A)  horizontal: $y = 4$; vertical: $x = 5$ 
B)  horizontal: $x = 0$; vertical: $y = 5$ 
C)  horizontal: $y = - 5$; vertical: $x = 0$ 
D)  horizontal: $x = 5$; vertical: $y = - 4$ 
E)  horizontal: $y = 0$; vertical: $x = 5$

Question 20

Use long division to divide. $$\left( x ^ { 4 } - 2 x ^ { 2 } - 1 \right) \div \left( x ^ { 2 } - 3 x - 2 \right)$$

Accepted Answer

A)  $x ^ { 2 } - 3 x + 3 + \frac { x - 2 } { x ^ { 2 } - 3 x - 2 }$ 
B)  $x ^ { 2 } + 3 x + 9 + \frac { 33 x + 17 } { x ^ { 2 } - 3 x - 2 }$ 
C)  $x ^ { 2 } - 3 x + 3$ 
D)  $x ^ { 2 } + 3 x - 3 - \frac { 4 } { x ^ { 2 } + 3 x - 3 }$ 
E)  $x ^ { 2 } + 3 x - 3$ 
A)  $x ^ { 2 } - 3 x + 3 + \frac { x - 2 } { x ^ { 2 } - 3 x - 2 }$ 
B)  $x ^ { 2 } + 3 x + 9 + \frac { 33 x + 17 } { x ^ { 2 } - 3 x - 2 }$ 
C)  $x ^ { 2 } - 3 x + 3$ 
D)  $x ^ { 2 } + 3 x - 3 - \frac { 4 } { x ^ { 2 } + 3 x - 3 }$ 
E)  $x ^ { 2 } + 3 x - 3$

Simplify the complex number and write it in standard form. $\frac { 1 } { ( 8 i ) ^ { 3 } }$

Find all the zeros of the function and write the polynomial as a product of linear fac- tors. $y ^ { 4 } - 16$

Solve the inequality and write the solution set in interval notation. $x ^ { 4 } ( x - 3 ) \leq 0$

Select the correct graph of the following function. $f ( x ) = \frac { x ^ { 2 } - 49 } { x + 7 }$

Perform the addition or subtraction and write the result in standard form. $( 3 + i ) + ( 4 - 3 i )$

Solve the inequality and graph the solution on the real number line $x ^ { 2 } \leq 16$

The total revenue $\ {R }$ earned per day (in dollars) from a pet-sitting service is given by $R ( p ) = - 12 p ^ { 2 } + 150 p$ where, $p$ is the price charged per pet (in dollars). Find the revenue when the price per pet is $\$ 9$ .

Describe the right-hand and the left-hand behavior of the graph of $\ { m ( x ) } = - 3 x ^ { 4 } + 2 x ^ { 3 } + 29$

Solve the inequality and write the solution set in interval notation. $x ^ { 5 } ( x - 4 ) \leq 0$

Select the correct graph of the following function. $f ( x ) = 6 x ^ { 3 } + x ^ { 2 } - 7 x + 4$

Select the correct graph of the following function. $f ( x ) = \frac { x ^ { 2 } - 25 } { x + 5 }$

Find all the rational zeros of the function $f ( x ) = 2 x ^ { 5 } - 9 x ^ { 4 } + 9 x ^ { 3 } - 3 x ^ { 2 } + 7 x + 6$

If $x = \sqrt { 7 } \text { is a root of } x ^ { 3 } - 3 x ^ { 2 } - 7 x + 21 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Perform the operation and write the result in standard form. $( 10 - 9 i ) ^ { 2 }$

Write the complex number in standard form. $\sqrt { - 9 }$

Select the correct graph of the functions f and g in the same viewing window. Zoom out sufficiently far to show that the right-hand and left-hand behaviors of and appear identical. $f ( x ) = x ^ { 3 } - 5 x + 1 , \quad g ( x ) = x ^ { 3 }$

Solve the inequality and graph the solution on the real number line $x ^ { 2 } \leq 16$

Find all the zeros of the function and write the polynomial as a product of linear fac- tors. $x ^ { 4 } + 29 x ^ { 2 } + 100$

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 4 } { x - 5 }$

Use long division to divide. $\left( x ^ { 4 } - 2 x ^ { 2 } - 1 \right) \div \left( x ^ { 2 } - 3 x - 2 \right)$

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Topics in Analytic Geometry

Filters

Exam 2: Polynomial and Rational Functions

Simplify the complex number and write it in standard form. 1(8i)3\frac { 1 } { ( 8 i ) ^ { 3 } }(8i)31​

Find all the zeros of the function and write the polynomial as a product of linear fac- tors. y4−16y ^ { 4 } - 16y4−16

Solve the inequality and write the solution set in interval notation. x4(x−3)≤0x ^ { 4 } ( x - 3 ) \leq 0x4(x−3)≤0

Select the correct graph of the following function. f(x)=x2−49x+7f ( x ) = \frac { x ^ { 2 } - 49 } { x + 7 }f(x)=x+7x2−49​

Perform the addition or subtraction and write the result in standard form. (3+i)+(4−3i)( 3 + i ) + ( 4 - 3 i )(3+i)+(4−3i)

Solve the inequality and graph the solution on the real number line x2≤16x ^ { 2 } \leq 16x2≤16

The total revenue R\ {R } R earned per day (in dollars) from a pet-sitting service is given by R(p)=−12p2+150pR ( p ) = - 12 p ^ { 2 } + 150 pR(p)=−12p2+150p where, ppp is the price charged per pet (in dollars). Find the revenue when the price per pet is $9\$ 9$9 .

Describe the right-hand and the left-hand behavior of the graph of m(x)=−3x4+2x3+29\ { m ( x ) } = - 3 x ^ { 4 } + 2 x ^ { 3 } + 29 m(x)=−3x4+2x3+29

Solve the inequality and write the solution set in interval notation. x5(x−4)≤0x ^ { 5 } ( x - 4 ) \leq 0x5(x−4)≤0

Select the correct graph of the following function. f(x)=6x3+x2−7x+4f ( x ) = 6 x ^ { 3 } + x ^ { 2 } - 7 x + 4f(x)=6x3+x2−7x+4

Select the correct graph of the following function. f(x)=x2−25x+5f ( x ) = \frac { x ^ { 2 } - 25 } { x + 5 }f(x)=x+5x2−25​

Find all the rational zeros of the function f(x)=2x5−9x4+9x3−3x2+7x+6f ( x ) = 2 x ^ { 5 } - 9 x ^ { 4 } + 9 x ^ { 3 } - 3 x ^ { 2 } + 7 x + 6f(x)=2x5−9x4+9x3−3x2+7x+6

If x=7 is a root of x3−3x2−7x+21=0x = \sqrt { 7 } \text { is a root of } x ^ { 3 } - 3 x ^ { 2 } - 7 x + 21 = 0x=7​ is a root of x3−3x2−7x+21=0 , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Perform the operation and write the result in standard form. (10−9i)2( 10 - 9 i ) ^ { 2 }(10−9i)2

Write the complex number in standard form. −9\sqrt { - 9 }−9​

Select the correct graph of the functions f and g in the same viewing window. Zoom out sufficiently far to show that the right-hand and left-hand behaviors of and appear identical. f(x)=x3−5x+1,g(x)=x3f ( x ) = x ^ { 3 } - 5 x + 1 , \quad g ( x ) = x ^ { 3 }f(x)=x3−5x+1,g(x)=x3

Solve the inequality and graph the solution on the real number line x2≤16x ^ { 2 } \leq 16x2≤16

Find all the zeros of the function and write the polynomial as a product of linear fac- tors. x4+29x2+100x ^ { 4 } + 29 x ^ { 2 } + 100x4+29x2+100

Determine the equations of the vertical and horizontal asymptotes of the graph of the function f(x)=4x−5f ( x ) = \frac { 4 } { x - 5 }f(x)=x−54​

Use long division to divide. (x4−2x2−1)÷(x2−3x−2)\left( x ^ { 4 } - 2 x ^ { 2 } - 1 \right) \div \left( x ^ { 2 } - 3 x - 2 \right)(x4−2x2−1)÷(x2−3x−2)

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Topics in Analytic Geometry

Filters

Simplify the complex number and write it in standard form. $\frac { 1 } { ( 8 i ) ^ { 3 } }$

Find all the zeros of the function and write the polynomial as a product of linear fac- tors. $y ^ { 4 } - 16$

Solve the inequality and write the solution set in interval notation. $x ^ { 4 } ( x - 3 ) \leq 0$

Select the correct graph of the following function. $f ( x ) = \frac { x ^ { 2 } - 49 } { x + 7 }$

Perform the addition or subtraction and write the result in standard form. $( 3 + i ) + ( 4 - 3 i )$

Solve the inequality and graph the solution on the real number line $x ^ { 2 } \leq 16$

The total revenue $\ {R }$ earned per day (in dollars) from a pet-sitting service is given by $R ( p ) = - 12 p ^ { 2 } + 150 p$ where, $p$ is the price charged per pet (in dollars). Find the revenue when the price per pet is $\$ 9$ .

Describe the right-hand and the left-hand behavior of the graph of $\ { m ( x ) } = - 3 x ^ { 4 } + 2 x ^ { 3 } + 29$

Solve the inequality and write the solution set in interval notation. $x ^ { 5 } ( x - 4 ) \leq 0$

Select the correct graph of the following function. $f ( x ) = 6 x ^ { 3 } + x ^ { 2 } - 7 x + 4$

Select the correct graph of the following function. $f ( x ) = \frac { x ^ { 2 } - 25 } { x + 5 }$

Find all the rational zeros of the function $f ( x ) = 2 x ^ { 5 } - 9 x ^ { 4 } + 9 x ^ { 3 } - 3 x ^ { 2 } + 7 x + 6$

If $x = \sqrt { 7 } \text { is a root of } x ^ { 3 } - 3 x ^ { 2 } - 7 x + 21 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Perform the operation and write the result in standard form. $( 10 - 9 i ) ^ { 2 }$

Write the complex number in standard form. $\sqrt { - 9 }$

Select the correct graph of the functions f and g in the same viewing window. Zoom out sufficiently far to show that the right-hand and left-hand behaviors of and appear identical. $f ( x ) = x ^ { 3 } - 5 x + 1 , \quad g ( x ) = x ^ { 3 }$

Solve the inequality and graph the solution on the real number line $x ^ { 2 } \leq 16$

Find all the zeros of the function and write the polynomial as a product of linear fac- tors. $x ^ { 4 } + 29 x ^ { 2 } + 100$

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 4 } { x - 5 }$

Use long division to divide. $\left( x ^ { 4 } - 2 x ^ { 2 } - 1 \right) \div \left( x ^ { 2 } - 3 x - 2 \right)$