Question 1

Perform the following operation and write the result in standard form.
$$\frac { 9 i } { 9 + i } + \frac { 2 } { 9 - i }$$

Accepted Answer

A)  $\frac { 9 } { 40 } + \frac { 83 } { 80 } i$ 
B)  $\frac { 27 } { 10 } + \frac { 83 } { 10 } i$ 
C)  $\frac { 1 } { 41 } + \frac { 9 } { 82 } i$ 
D)  $\frac { 27 } { 82 } + \frac { 83 } { 82 } i$ 
E)  $\frac { 27 } { 8 } + \frac { 83 } { 8 } i$ 
A)  $\frac { 9 } { 40 } + \frac { 83 } { 80 } i$ 
B)  $\frac { 27 } { 10 } + \frac { 83 } { 10 } i$ 
C)  $\frac { 1 } { 41 } + \frac { 9 } { 82 } i$ 
D)  $\frac { 27 } { 82 } + \frac { 83 } { 82 } i$ 
E)  $\frac { 27 } { 8 } + \frac { 83 } { 8 } i$ D

Question 2

Determine the domain of $f ( x ) = \frac { 6 x + 6 } { x ^ { 2 } - 6 x }$.

Accepted Answer

A)  all real numbers except $x = - 1 , x = 0$, and $x = 6$ 
B)  all real numbers except $x = 0$ and $x = 6$ 
C)  all real numbers except $x = - 6$ and $x = - 1$ 
D)  all real numbers except $x = 6$ 
E)  all real numbers 
A)  all real numbers except $x = - 1 , x = 0$, and $x = 6$ 
B)  all real numbers except $x = 0$ and $x = 6$ 
C)  all real numbers except $x = - 6$ and $x = - 1$ 
D)  all real numbers except $x = 6$ 
E)  all real numbers B

Question 3

Compare the graph of $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ with $s ( x ) = x ^ { 2 }$.

Accepted Answer

A)  $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ shifts right 5 units, shifts downward 9 units, and shrinks by a factor of $\frac { 1 } { 5 }$. 
B)  $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ shifts right 5 units, shifts upward 9 units, and stretches by a factor of 5 . 
C)  $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ shifts left 5 units, shifts downward 9 units, and stretches by a factor of 5 . 
D)  $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ shifts right 5 units, shifts upward 9 units, and shrinks by a factor of $\frac { 1 } { 5 }$. 
E)  $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ shifts left 5 units, shifts upward 9 units, and stretches by a factor of 5 . 
A)  $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ shifts right 5 units, shifts downward 9 units, and shrinks by a factor of $\frac { 1 } { 5 }$. 
B)  $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ shifts right 5 units, shifts upward 9 units, and stretches by a factor of 5 . 
C)  $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ shifts left 5 units, shifts downward 9 units, and stretches by a factor of 5 . 
D)  $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ shifts right 5 units, shifts upward 9 units, and shrinks by a factor of $\frac { 1 } { 5 }$. 
E)  $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ shifts left 5 units, shifts upward 9 units, and stretches by a factor of 5 . B

Question 4

Find real numbers $a$ and $b$ such that the equation $a + b i = 4 - 9 i$ is true.

Accepted Answer

A)  $\quad a = - 4 , b = 9$ 
B)  $\quad a = 4 , b = 9$ 
C)  $\quad a = - 4 , b = - 9$ 
D)  $a = 4 , b = - 9$ 
E)  $\quad a = 13 , b = - 5$ 
A)  $\quad a = - 4 , b = 9$ 
B)  $\quad a = 4 , b = 9$ 
C)  $\quad a = - 4 , b = - 9$ 
D)  $a = 4 , b = - 9$ 
E)  $\quad a = 13 , b = - 5$

Question 5

Write $f ( x ) = x ^ { 4 } - 12 x ^ { 3 } + 59 x ^ { 2 } - 138 x + 130$ as a product of linear factors.

Accepted Answer

A)  $( x - 3 - i ) ( x - 3 + 2 i ) ( x - 3 - 2 i ) ( x - 2 + i )$ 
B)  $( x - 3 - i ) ( x - 3 + i ) ( x - 2 - i ) ( x - 2 + i )$ 
C)  $( x - 3 - i ) ( x - 3 + i ) ( x + 3 - 2 i ) ( x - 2 + i )$ 
D)  $( x - 3 + i ) ( x - 3 - i ) ( x - 2 + 3 i ) ( x - 2 - 3 i )$ 
E)  $( x - 3 + i ) ( x - 3 - i ) ( x - 3 + 2 i ) ( x - 3 - 2 i )$ 
A)  $( x - 3 - i ) ( x - 3 + 2 i ) ( x - 3 - 2 i ) ( x - 2 + i )$ 
B)  $( x - 3 - i ) ( x - 3 + i ) ( x - 2 - i ) ( x - 2 + i )$ 
C)  $( x - 3 - i ) ( x - 3 + i ) ( x + 3 - 2 i ) ( x - 2 + i )$ 
D)  $( x - 3 + i ) ( x - 3 - i ) ( x - 2 + 3 i ) ( x - 2 - 3 i )$ 
E)  $( x - 3 + i ) ( x - 3 - i ) ( x - 3 + 2 i ) ( x - 3 - 2 i )$

Question 6

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

Accepted Answer

A)  $x ^ { 2 } - 2 x + 8 - \frac { 17 } { x + 2 }$ 
B)  $x ^ { 2 } + 2 x + 8 - \frac { 15 } { x + 2 }$ 
C)  $x ^ { 2 } + 2 - \frac { 3 } { x + 2 }$ 
D)  $x ^ { 2 } - 2 + \frac { 3 } { x + 2 }$ 
E)  $x ^ { 2 } + 2 x - 8 + \frac { 17 } { x + 2 }$ 
A)  $x ^ { 2 } - 2 x + 8 - \frac { 17 } { x + 2 }$ 
B)  $x ^ { 2 } + 2 x + 8 - \frac { 15 } { x + 2 }$ 
C)  $x ^ { 2 } + 2 - \frac { 3 } { x + 2 }$ 
D)  $x ^ { 2 } - 2 + \frac { 3 } { x + 2 }$ 
E)  $x ^ { 2 } + 2 x - 8 + \frac { 17 } { x + 2 }$

Question 7

Find a polynomial function with following characteristics.
Degree: 4
Zero: $ -1 $, multiplicity: 2
Zero: $ -3 $, multiplicity: 2
Falls to the left,
Falls to the right
Absolute value of the leading coefficient is one

Accepted Answer

A)  $y = x ^ { 4 } - 4 x ^ { 3 } + 22 x ^ { 2 } + 24 x + 3$ 
B)  $y = - x ^ { 4 } - 4 x ^ { 3 } + 12 x ^ { 2 } + 9$ 
C)  $y = x ^ { 4 } - 6 x ^ { 3 } - 18 x ^ { 2 } + 10 x + 3$ 
D)  $y = - x ^ { 4 } - 8 x ^ { 3 } - 22 x ^ { 2 } - 24 x - 9$ 
E)  $y = - x ^ { 4 } - 8 x ^ { 3 } - 24 x + 9$ 
A)  $y = x ^ { 4 } - 4 x ^ { 3 } + 22 x ^ { 2 } + 24 x + 3$ 
B)  $y = - x ^ { 4 } - 4 x ^ { 3 } + 12 x ^ { 2 } + 9$ 
C)  $y = x ^ { 4 } - 6 x ^ { 3 } - 18 x ^ { 2 } + 10 x + 3$ 
D)  $y = - x ^ { 4 } - 8 x ^ { 3 } - 22 x ^ { 2 } - 24 x - 9$ 
E)  $y = - x ^ { 4 } - 8 x ^ { 3 } - 24 x + 9$

Question 8

Using the factors $( x + 4 )$ and $( x + 3 )$, find the remaining factor(s) of $f ( x ) = x ^ { 3 } + 6 x ^ { 2 } + 5 x - 12$ and write the polynomial in fully factored form.

Accepted Answer

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

Question 9

Describe the right-hand and the left-hand behavior of the graph of
$$t ( x ) = - \frac { 4 } { 7 } \left( x ^ { 3 } + 5 x ^ { 2 } + 8 x + 1 \right) .$$

Accepted Answer

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

Question 10

Determine whether the scatter plot could best be modeled by a linear model, a quadratic model, or neither.

Accepted Answer

A)  linear model 
B)  quadratic model 
C)  neither 
A)  linear model 
B)  quadratic model 
C)  neither

Question 11

Simplify $\frac { - 1 - 5 i } { 7 i }$ and write the answer in standard form.

Accepted Answer

A)  $\frac { 5 } { 7 } + \frac { i } { 7 }$ 
B)  $- \frac { 5 } { 7 } + \frac { i } { 7 }$ 
C)  $- \frac { 5 } { 7 } - \frac { i } { 7 }$ 
D)  $- \frac { 1 } { 7 } - \frac { 5 i } { 7 }$ 
E)  $\frac { 1 } { 7 } - \frac { 5 i } { 7 }$ 
A)  $\frac { 5 } { 7 } + \frac { i } { 7 }$ 
B)  $- \frac { 5 } { 7 } + \frac { i } { 7 }$ 
C)  $- \frac { 5 } { 7 } - \frac { i } { 7 }$ 
D)  $- \frac { 1 } { 7 } - \frac { 5 i } { 7 }$ 
E)  $\frac { 1 } { 7 } - \frac { 5 i } { 7 }$

Question 12

Simplify $( \sqrt { - 2 } ) ^ { 11 }$ and write the answer in standard form.

Accepted Answer

A)  $32 \sqrt { 2 } i$ 
B)  $- 32 \sqrt { 2 } i$ 
C)  $1024 \sqrt { 2 } i$ 
D)  $- 32 \sqrt { 2 }$ 
E)  The expression cannot be simplified. 
A)  $32 \sqrt { 2 } i$ 
B)  $- 32 \sqrt { 2 } i$ 
C)  $1024 \sqrt { 2 } i$ 
D)  $- 32 \sqrt { 2 }$ 
E)  The expression cannot be simplified.

Question 13

Find the zeros of the function below algebraically, if any exist.
$$f ( t ) = \frac { 1 } { 6 } t ^ { 4 } - \frac { 27 } { 2 }$$

Accepted Answer

A)  $- 3 , - 1,1$, and 3 
B)  $- 3$ and 3 
C)  $- 6$ and 6 
D)  $- 6 , - 1,1$, and 6 
E)  No zeros exist. 
A)  $- 3 , - 1,1$, and 3 
B)  $- 3$ and 3 
C)  $- 6$ and 6 
D)  $- 6 , - 1,1$, and 6 
E)  No zeros exist.

Question 14

Find the zeros of the function below algebraically, if any exist. $f ( x ) = 2 x ^ { 4 } + 10 x ^ { 2 } + 12$

Accepted Answer

A)  $- \sqrt { 3 } , - \sqrt { 2 } , \sqrt { 2 }$, and $\sqrt { 3 }$ 
B)  $- \sqrt { 3 } , 0$, and $\sqrt { 3 }$ 
C)  $- \sqrt { 3 }$ and $\sqrt { 3 }$ 
D)  $- \sqrt { 2 }$ and $\sqrt { 2 }$ 
E)  No zeros exist. 
A)  $- \sqrt { 3 } , - \sqrt { 2 } , \sqrt { 2 }$, and $\sqrt { 3 }$ 
B)  $- \sqrt { 3 } , 0$, and $\sqrt { 3 }$ 
C)  $- \sqrt { 3 }$ and $\sqrt { 3 }$ 
D)  $- \sqrt { 2 }$ and $\sqrt { 2 }$ 
E)  No zeros exist.

Question 15

The graph of the function
$$f ( x ) = \frac { 3 x } { x + 1 }$$
is shown below. Determine the domain.

Accepted Answer

A)  Domain: all real numbers except $x = - 1$ 
B)  Domain: all real numbers except $x = - 1$ and $x = 0$ 
C)  Domain: all real numbers except $x = - 1$ and $x = 3$ 
D)  Domain: all real numbers except $x = 3$ 
E)  Domain: all real numbers except $x = 0$ 
A)  Domain: all real numbers except $x = - 1$ 
B)  Domain: all real numbers except $x = - 1$ and $x = 0$ 
C)  Domain: all real numbers except $x = - 1$ and $x = 3$ 
D)  Domain: all real numbers except $x = 3$ 
E)  Domain: all real numbers except $x = 0$

Question 16

Which of the given graphs is the graph of the polynomial function below?
$h ( x ) = x ^ { 5 } - \frac { 3 } { 2 } x ^ { 3 } - \frac { 1 } { 2 } x$
Graph 1:
 
Graph 2 :
 
Graph 3:
 
Graph 4 :
 
 Graph 5:

Accepted Answer

A)  Graph 2 
B)  Graph 5 
C)  Graph 4 
D)  Graph 1 
E)  Graph 3 
A)  Graph 2 
B)  Graph 5 
C)  Graph 4 
D)  Graph 1 
E)  Graph 3

Question 17

Sketch the graph of the rational function below. $f ( x ) = \frac { x ^ { 2 } - 1 } { x }$

Accepted Answer

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

Question 18

Given $3 + i$ is a root, determine all other roots of $f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 42 x ^ { 2 } - 88 x + 80$.

Accepted Answer

A)  $x = 3 + i , 2 \pm 2 i , 2 - i$ 
B)  $x = 3 - i , 2 \pm i$ 
C)  $x = 3 - i , 2 - 2 i , 2 + i$ 
D)  $x = 3 - i , - 2 \pm 2 i$ 
E)  $x = 3 - i , 2 \pm 2 i$ 
A)  $x = 3 + i , 2 \pm 2 i , 2 - i$ 
B)  $x = 3 - i , 2 \pm i$ 
C)  $x = 3 - i , 2 - 2 i , 2 + i$ 
D)  $x = 3 - i , - 2 \pm 2 i$ 
E)  $x = 3 - i , 2 \pm 2 i$

Question 19

Find all the rational zeros of the function
$$f ( x ) = - 2 x ^ { 5 } - 11 x ^ { 4 } - 19 x ^ { 3 } - 17 x ^ { 2 } - 17 x - 6 .$$

Accepted Answer

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

Question 20

Use synthetic division to divide.
$$\left( 2 x ^ { 3 } - 5 x ^ { 2 } - 22 x - 15 \right) \div ( x - 5 )$$

Accepted Answer

A)  $2 x ^ { 2 } - 3 x - 5$ 
B)  $2 x ^ { 2 } + 5 x + 3$ 
C)  $2 x ^ { 2 } - 2 x - 15$ 
D)  $2 x ^ { 2 } - 7 x + 6$ 
E)  $2 x ^ { 2 } + 5 x + 2$ 
A)  $2 x ^ { 2 } - 3 x - 5$ 
B)  $2 x ^ { 2 } + 5 x + 3$ 
C)  $2 x ^ { 2 } - 2 x - 15$ 
D)  $2 x ^ { 2 } - 7 x + 6$ 
E)  $2 x ^ { 2 } + 5 x + 2$

Perform the following operation and write the result in standard form. $\frac { 9 i } { 9 + i } + \frac { 2 } { 9 - i }$

Determine the domain of $f ( x ) = \frac { 6 x + 6 } { x ^ { 2 } - 6 x }$ .

Compare the graph of $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ with $s ( x ) = x ^ { 2 }$ .

Find real numbers $a$ and $b$ such that the equation $a + b i = 4 - 9 i$ is true.

Write $f ( x ) = x ^ { 4 } - 12 x ^ { 3 } + 59 x ^ { 2 } - 138 x + 130$ as a product of linear factors.

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

Find a polynomial function with following characteristics. Degree: 4 Zero: $-1$ , multiplicity: 2 Zero: $-3$ , multiplicity: 2 Falls to the left, Falls to the right Absolute value of the leading coefficient is one

Using the factors $( x + 4 )$ and $( x + 3 )$ , find the remaining factor(s) of $f ( x ) = x ^ { 3 } + 6 x ^ { 2 } + 5 x - 12$ and write the polynomial in fully factored form.

Describe the right-hand and the left-hand behavior of the graph of $t ( x ) = - \frac { 4 } { 7 } \left( x ^ { 3 } + 5 x ^ { 2 } + 8 x + 1 \right) .$

Determine whether the scatter plot could best be modeled by a linear model, a quadratic model, or neither.

Simplify $\frac { - 1 - 5 i } { 7 i }$ and write the answer in standard form.

Simplify $( \sqrt { - 2 } ) ^ { 11 }$ and write the answer in standard form.

Find the zeros of the function below algebraically, if any exist. $f ( t ) = \frac { 1 } { 6 } t ^ { 4 } - \frac { 27 } { 2 }$

Find the zeros of the function below algebraically, if any exist. $f ( x ) = 2 x ^ { 4 } + 10 x ^ { 2 } + 12$

The graph of the function $f ( x ) = \frac { 3 x } { x + 1 }$ is shown below. Determine the domain. $The graph of the function f ( x ) = \frac { 3 x } { x + 1 } is shown below. Determine the domain.$

Sketch the graph of the rational function below. $f ( x ) = \frac { x ^ { 2 } - 1 } { x }$

Given $3 + i$ is a root, determine all other roots of $f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 42 x ^ { 2 } - 88 x + 80$ .

Find all the rational zeros of the function $f ( x ) = - 2 x ^ { 5 } - 11 x ^ { 4 } - 19 x ^ { 3 } - 17 x ^ { 2 } - 17 x - 6 .$

Use synthetic division to divide. $\left( 2 x ^ { 3 } - 5 x ^ { 2 } - 22 x - 15 \right) \div ( x - 5 )$

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

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

Perform the following operation and write the result in standard form. 9i9+i+29−i\frac { 9 i } { 9 + i } + \frac { 2 } { 9 - i }9+i9i​+9−i2​

Determine the domain of f(x)=6x+6x2−6xf ( x ) = \frac { 6 x + 6 } { x ^ { 2 } - 6 x }f(x)=x2−6x6x+6​ .

Compare the graph of s(x)=5(x−5)2+9s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9s(x)=5(x−5)2+9 with s(x)=x2s ( x ) = x ^ { 2 }s(x)=x2 .

Find real numbers aaa and bbb such that the equation a+bi=4−9ia + b i = 4 - 9 ia+bi=4−9i is true.

Write f(x)=x4−12x3+59x2−138x+130f ( x ) = x ^ { 4 } - 12 x ^ { 3 } + 59 x ^ { 2 } - 138 x + 130f(x)=x4−12x3+59x2−138x+130 as a product of linear factors.

Use long division to divide. (x3+4x−1)÷(x+2)\left( x ^ { 3 } + 4 x - 1 \right) \div ( x + 2 )(x3+4x−1)÷(x+2)

Find a polynomial function with following characteristics. Degree: 4 Zero: −1 -1 −1 , multiplicity: 2 Zero: −3 -3 −3 , multiplicity: 2 Falls to the left, Falls to the right Absolute value of the leading coefficient is one

Using the factors (x+4)( x + 4 )(x+4) and (x+3)( x + 3 )(x+3) , find the remaining factor(s) of f(x)=x3+6x2+5x−12f ( x ) = x ^ { 3 } + 6 x ^ { 2 } + 5 x - 12f(x)=x3+6x2+5x−12 and write the polynomial in fully factored form.

Describe the right-hand and the left-hand behavior of the graph of t(x)=−47(x3+5x2+8x+1).t ( x ) = - \frac { 4 } { 7 } \left( x ^ { 3 } + 5 x ^ { 2 } + 8 x + 1 \right) .t(x)=−74​(x3+5x2+8x+1).

Determine whether the scatter plot could best be modeled by a linear model, a quadratic model, or neither.

Simplify −1−5i7i\frac { - 1 - 5 i } { 7 i }7i−1−5i​ and write the answer in standard form.

Simplify (−2)11( \sqrt { - 2 } ) ^ { 11 }(−2​)11 and write the answer in standard form.

Find the zeros of the function below algebraically, if any exist. f(t)=16t4−272f ( t ) = \frac { 1 } { 6 } t ^ { 4 } - \frac { 27 } { 2 }f(t)=61​t4−227​

Find the zeros of the function below algebraically, if any exist. f(x)=2x4+10x2+12f ( x ) = 2 x ^ { 4 } + 10 x ^ { 2 } + 12f(x)=2x4+10x2+12

The graph of the function f(x)=3xx+1f ( x ) = \frac { 3 x } { x + 1 }f(x)=x+13x​ is shown below. Determine the domain.

Which of the given graphs is the graph of the polynomial function below? h(x)=x5−32x3−12xh ( x ) = x ^ { 5 } - \frac { 3 } { 2 } x ^ { 3 } - \frac { 1 } { 2 } xh(x)=x5−23​x3−21​x Graph 1: Graph 2 : Graph 3: Graph 4 : Graph 5:

Sketch the graph of the rational function below. f(x)=x2−1xf ( x ) = \frac { x ^ { 2 } - 1 } { x }f(x)=xx2−1​

Given 3+i3 + i3+i is a root, determine all other roots of f(x)=x4−10x3+42x2−88x+80f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 42 x ^ { 2 } - 88 x + 80f(x)=x4−10x3+42x2−88x+80 .

Find all the rational zeros of the function f(x)=−2x5−11x4−19x3−17x2−17x−6.f ( x ) = - 2 x ^ { 5 } - 11 x ^ { 4 } - 19 x ^ { 3 } - 17 x ^ { 2 } - 17 x - 6 .f(x)=−2x5−11x4−19x3−17x2−17x−6.

Use synthetic division to divide. (2x3−5x2−22x−15)÷(x−5)\left( 2 x ^ { 3 } - 5 x ^ { 2 } - 22 x - 15 \right) \div ( x - 5 )(2x3−5x2−22x−15)÷(x−5)

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Filters

Perform the following operation and write the result in standard form. $\frac { 9 i } { 9 + i } + \frac { 2 } { 9 - i }$

Determine the domain of $f ( x ) = \frac { 6 x + 6 } { x ^ { 2 } - 6 x }$ .

Compare the graph of $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ with $s ( x ) = x ^ { 2 }$ .

Find real numbers $a$ and $b$ such that the equation $a + b i = 4 - 9 i$ is true.

Write $f ( x ) = x ^ { 4 } - 12 x ^ { 3 } + 59 x ^ { 2 } - 138 x + 130$ as a product of linear factors.

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

Find a polynomial function with following characteristics. Degree: 4 Zero: $-1$ , multiplicity: 2 Zero: $-3$ , multiplicity: 2 Falls to the left, Falls to the right Absolute value of the leading coefficient is one

Using the factors $( x + 4 )$ and $( x + 3 )$ , find the remaining factor(s) of $f ( x ) = x ^ { 3 } + 6 x ^ { 2 } + 5 x - 12$ and write the polynomial in fully factored form.

Describe the right-hand and the left-hand behavior of the graph of $t ( x ) = - \frac { 4 } { 7 } \left( x ^ { 3 } + 5 x ^ { 2 } + 8 x + 1 \right) .$

Simplify $\frac { - 1 - 5 i } { 7 i }$ and write the answer in standard form.

Simplify $( \sqrt { - 2 } ) ^ { 11 }$ and write the answer in standard form.

Find the zeros of the function below algebraically, if any exist. $f ( t ) = \frac { 1 } { 6 } t ^ { 4 } - \frac { 27 } { 2 }$

Find the zeros of the function below algebraically, if any exist. $f ( x ) = 2 x ^ { 4 } + 10 x ^ { 2 } + 12$

The graph of the function $f ( x ) = \frac { 3 x } { x + 1 }$ is shown below. Determine the domain. $The graph of the function f ( x ) = \frac { 3 x } { x + 1 } is shown below. Determine the domain.$

Sketch the graph of the rational function below. $f ( x ) = \frac { x ^ { 2 } - 1 } { x }$

Given $3 + i$ is a root, determine all other roots of $f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 42 x ^ { 2 } - 88 x + 80$ .

Find all the rational zeros of the function $f ( x ) = - 2 x ^ { 5 } - 11 x ^ { 4 } - 19 x ^ { 3 } - 17 x ^ { 2 } - 17 x - 6 .$

Use synthetic division to divide. $\left( 2 x ^ { 3 } - 5 x ^ { 2 } - 22 x - 15 \right) \div ( x - 5 )$