Question 1

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 13 x ^ { 3 } + 40 x ^ { 2 }$ and determine the mutiplicity of each.

Accepted Answer

A)  $x = 0$, multiplicity $2 ; x = - 8$, multiplicity $1 ; x = - 5$, multiplicity 1 
B)  $x = 8$, multiplicity $2 ; x = 5$, multiplicity 2 
C)  $x = 0$, multiplicity $2 ; x = 8$, multiplicity $1 ; x = 5$, multiplicity 1 
D)  $x = - 8$, multiplicity $2 ; x = - 5$, multiplicity 2 
E)  $x = 0$, multiplicity $1 ; x = 8$, multiplicity $1 ; x = - 8$, multiplicity $1 ; x = 5$, multiplicity 1 
A)  $x = 0$, multiplicity $2 ; x = - 8$, multiplicity $1 ; x = - 5$, multiplicity 1 
B)  $x = 8$, multiplicity $2 ; x = 5$, multiplicity 2 
C)  $x = 0$, multiplicity $2 ; x = 8$, multiplicity $1 ; x = 5$, multiplicity 1 
D)  $x = - 8$, multiplicity $2 ; x = - 5$, multiplicity 2 
E)  $x = 0$, multiplicity $1 ; x = 8$, multiplicity $1 ; x = - 8$, multiplicity $1 ; x = 5$, multiplicity 1 A

Question 2

Match the equation with its graph.
$f ( x ) = x ^ { 2 } + 2 x - 3$

Accepted Answer

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

Question 3

Find the zeros of the function below algebraically, if any exist.
$f ( x ) = x ^ { 5 } - 5 x ^ { 3 } + 4 x$

Accepted Answer

A)  $- 4 , - 1,1,4$ 
B)  $- 4 , - 2,2,4$ 
C)  $- 2 , - 1,0,1,2$ 
D)  $- 4 , - 2,0,2,4$ 
E)  No zeros exist. 
A)  $- 4 , - 1,1,4$ 
B)  $- 4 , - 2,2,4$ 
C)  $- 2 , - 1,0,1,2$ 
D)  $- 4 , - 2,0,2,4$ 
E)  No zeros exist. C

Question 4

Write the complex conjugate of the following complex number and then multiply the number by the complex conjugate. Write the result in standard form.
$2 + \sqrt { - 27 }$

Accepted Answer

A)  $2 - 27 i ; 25$ 
B)  $2 - 3 \sqrt { 3 } i ; \quad 31$ 
C)  $- 2 - 3 \sqrt { 3 } i ; 31$ 
D)  $- 2 - 3 \sqrt { 3 } i ; \quad 25$ 
E)  $\quad 2 - 3 \sqrt { 3 } i ; \quad 31$ 
A)  $2 - 27 i ; 25$ 
B)  $2 - 3 \sqrt { 3 } i ; \quad 31$ 
C)  $- 2 - 3 \sqrt { 3 } i ; 31$ 
D)  $- 2 - 3 \sqrt { 3 } i ; \quad 25$ 
E)  $\quad 2 - 3 \sqrt { 3 } i ; \quad 31$

Question 5

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
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 6

Use long division to divide.
$$\left( x ^ { 4 } - x ^ { 2 } - 5 \right) \div \left( x ^ { 2 } + 4 x - 1 \right)$$

Accepted Answer

A)  $x ^ { 2 } - 4 x + 4$ 
B)  $x ^ { 2 } + 4 x - 4$ 
C)  $x ^ { 2 } - 4 x + 16 + \frac { - 68 x + 11 } { x ^ { 2 } + 4 x - 1 }$ 
D)  $x ^ { 2 } + 4 x - 4 + \frac { - 5 x - 1 } { x ^ { 2 } + 4 x - 1 }$ 
E)  $x ^ { 2 } - 4 x + 4 - \frac { 4 } { x ^ { 2 } - 4 x + 4 }$ 
A)  $x ^ { 2 } - 4 x + 4$ 
B)  $x ^ { 2 } + 4 x - 4$ 
C)  $x ^ { 2 } - 4 x + 16 + \frac { - 68 x + 11 } { x ^ { 2 } + 4 x - 1 }$ 
D)  $x ^ { 2 } + 4 x - 4 + \frac { - 5 x - 1 } { x ^ { 2 } + 4 x - 1 }$ 
E)  $x ^ { 2 } - 4 x + 4 - \frac { 4 } { x ^ { 2 } - 4 x + 4 }$

Question 7

Identify any horizontal and vertical asymptotes of the function below.
$$f ( x ) = \frac { 2 x - 8 } { | x | + 6 }$$

Accepted Answer

A)  vertical asymptotes: $x = - 2$ and $x = 2$; horizontal asymptotes: $y = - 6$ and $y = 6$ 
B)  vertical asymptotes: $x = - 2$ and $x = 2$; horizontal asymptotes: none 
C)  vertical asymptotes: $x = - 6$ and $x = 6$; horizontal asymptotes: none 
D)  vertical asymptotes: none; horizontal asymptotes: $y = - 2$ and $y = 2$ 
E)  vertical asymptotes: $x = - 6$ and $x = 6$; horizontal asymptotes: $y = - 2$ and $y = 2$ 
A)  vertical asymptotes: $x = - 2$ and $x = 2$; horizontal asymptotes: $y = - 6$ and $y = 6$ 
B)  vertical asymptotes: $x = - 2$ and $x = 2$; horizontal asymptotes: none 
C)  vertical asymptotes: $x = - 6$ and $x = 6$; horizontal asymptotes: none 
D)  vertical asymptotes: none; horizontal asymptotes: $y = - 2$ and $y = 2$ 
E)  vertical asymptotes: $x = - 6$ and $x = 6$; horizontal asymptotes: $y = - 2$ and $y = 2$

Question 8

Determine the domain of $f ( x ) = \frac { 3 x + 3 } { x ^ { 2 } - 3 x }$.

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Find two positive real numbers whose product is a maximum and whose sum of the first number and four times the second is 200 .

Accepted Answer

A)  160, 10 
B)  116, 21 
C)  108, 23 
D)  100, 25 
E)  76, 31 
A)  160, 10 
B)  116, 21 
C)  108, 23 
D)  100, 25 
E)  76, 31

Question 11

Simplify $f$ below and find any vertical asymptotes of $f$.
$$f ( x ) = \frac { x ^ { 2 } - 25 } { x + 5 }$$

Accepted Answer

A)  $f ( x ) = x + 5 , x \neq 5$; vertical asymptotes: none 
B)  $f ( x ) = x - 5 , x \neq - 5$; vertical asymptotes: none 
C)  $f ( x ) = x - 5 , x \neq 5$; vertical asymptotes: none 
D)  $f ( x ) = x + 5 , x \neq - 5$; vertical asymptotes: $x =- 5$ 
E)  $f ( x ) = x - 5 , x \neq 5$; vertical asymptotes: $x = 5$ 
A)  $f ( x ) = x + 5 , x \neq 5$; vertical asymptotes: none 
B)  $f ( x ) = x - 5 , x \neq - 5$; vertical asymptotes: none 
C)  $f ( x ) = x - 5 , x \neq 5$; vertical asymptotes: none 
D)  $f ( x ) = x + 5 , x \neq - 5$; vertical asymptotes: $x =- 5$ 
E)  $f ( x ) = x - 5 , x \neq 5$; vertical asymptotes: $x = 5$

Question 12

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

Question 13

Find the quadratic function $f$ whose graph intersects the $x$-axis at $( 2,0 )$ and $( 3,0 )$ and the $y$-axis at $( 0 , - 18 )$.

Accepted Answer

A)  $f ( x ) = 3 x ^ { 2 } + 3 x + 9$ 
B)  $f ( x ) = - 3 x ^ { 2 } + 15 x - 18$ 
C)  $f ( x ) = - 3 x ^ { 2 } - 3 x + 6$ 
D)  $f ( x ) = 3 x ^ { 2 } - 3 x - 18$ 
E)  $f ( x ) = 3 x ^ { 2 } - 15 x - 18$ 
A)  $f ( x ) = 3 x ^ { 2 } + 3 x + 9$ 
B)  $f ( x ) = - 3 x ^ { 2 } + 15 x - 18$ 
C)  $f ( x ) = - 3 x ^ { 2 } - 3 x + 6$ 
D)  $f ( x ) = 3 x ^ { 2 } - 3 x - 18$ 
E)  $f ( x ) = 3 x ^ { 2 } - 15 x - 18$

Question 14

Find all zeros of the function $f ( x ) = ( x + 6 ) ( x + 3 i ) ( x - 3 i )$.

Accepted Answer

A)  $x = 6 , - 3 i , 3 i$ 
B)  $x = - 6,3 i$ 
C)  $x = - 6 , - 3,3$ 
D)  $x = - 6 , - 3 i , 3 i$ 
E)  $x = - 6$ 
A)  $x = 6 , - 3 i , 3 i$ 
B)  $x = - 6,3 i$ 
C)  $x = - 6 , - 3,3$ 
D)  $x = - 6 , - 3 i , 3 i$ 
E)  $x = - 6$

Question 15

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

Accepted Answer

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

Question 16

Find a polynomial function of the lowest degree with real coefficients that has the zeros below and whose leading coefficient is one.
$0 , - 3,1 + 3 i$

Accepted Answer

A)  $f ( x ) = x ^ { 4 } + 30 x ^ { 3 } - 5 x ^ { 2 } + x$ 
B)  $f ( x ) = x ^ { 4 } + x ^ { 3 } + 4 x ^ { 2 } + 30 x$ 
C)  $f ( x ) = x ^ { 4 } - 5 x ^ { 3 } + x ^ { 2 } + 30 x$ 
D)  $f ( x ) = x ^ { 4 } + x ^ { 3 } + 30 x ^ { 2 } - 5 x$ 
E)  $f ( x ) = x ^ { 4 } - 5 x ^ { 3 } + 30 x ^ { 2 } + x$ 
A)  $f ( x ) = x ^ { 4 } + 30 x ^ { 3 } - 5 x ^ { 2 } + x$ 
B)  $f ( x ) = x ^ { 4 } + x ^ { 3 } + 4 x ^ { 2 } + 30 x$ 
C)  $f ( x ) = x ^ { 4 } - 5 x ^ { 3 } + x ^ { 2 } + 30 x$ 
D)  $f ( x ) = x ^ { 4 } + x ^ { 3 } + 30 x ^ { 2 } - 5 x$ 
E)  $f ( x ) = x ^ { 4 } - 5 x ^ { 3 } + 30 x ^ { 2 } + x$

Question 17

Find real numbers $a$ and $b$ such that the equation $a + b i = - 10 + 10 i$ is true.

Accepted Answer

A)  $\quad a = 10 , b = - 10$ 
B)  $a = - 10 , b = - 10$ 
C)  $\quad a = 10 , b = 10$ 
D)  $\quad a = - 10 , b = 10$ 
E)  $\quad a = - 20 , b = 0$ 
A)  $\quad a = 10 , b = - 10$ 
B)  $a = - 10 , b = - 10$ 
C)  $\quad a = 10 , b = 10$ 
D)  $\quad a = - 10 , b = 10$ 
E)  $\quad a = - 20 , b = 0$

Question 18

Compare the graph of $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ with $s ( x ) = x ^ { 2 }$.
$s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ shifts right 5 units, shifts downward 9 units, and shrinks by a

Accepted Answer

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)  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 .

Question 19

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 20

Determine the $x$-intercept(s) of the quadratic function 
$f ( x ) = x ^ { 2 } - 10 x + 26$.

Accepted Answer

A)  $( 0,0 ) , ( 4,0 )$ 
B)  $( 5,0 ) , ( 10,0 )$ 
C)  $( 7,0 ) , ( 2,0 )$ 
D)  $( 0,0 ) , ( 2,0 )$ 
E)  no $x$-intercept(s) 
A)  $( 0,0 ) , ( 4,0 )$ 
B)  $( 5,0 ) , ( 10,0 )$ 
C)  $( 7,0 ) , ( 2,0 )$ 
D)  $( 0,0 ) , ( 2,0 )$ 
E)  no $x$-intercept(s)

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 13 x ^ { 3 } + 40 x ^ { 2 }$ and determine the mutiplicity of each.

Match the equation with its graph. $f ( x ) = x ^ { 2 } + 2 x - 3$

Find the zeros of the function below algebraically, if any exist. $f ( x ) = x ^ { 5 } - 5 x ^ { 3 } + 4 x$

Write the complex conjugate of the following complex number and then multiply the number by the complex conjugate. Write the result in standard form. $2 + \sqrt { - 27 }$

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 Absolute value of the leading coefficient is one

Use long division to divide. $\left( x ^ { 4 } - x ^ { 2 } - 5 \right) \div \left( x ^ { 2 } + 4 x - 1 \right)$

Identify any horizontal and vertical asymptotes of the function below. $f ( x ) = \frac { 2 x - 8 } { | x | + 6 }$

Determine the domain of $f ( x ) = \frac { 3 x + 3 } { x ^ { 2 } - 3 x }$ .

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

Find two positive real numbers whose product is a maximum and whose sum of the first number and four times the second is 200 .

Simplify $f$ below and find any vertical asymptotes of $f$ . $f ( x ) = \frac { x ^ { 2 } - 25 } { x + 5 }$

Find the quadratic function $f$ whose graph intersects the $x$ -axis at $( 2,0 )$ and $( 3,0 )$ and the $y$ -axis at $( 0 , - 18 )$ .

Find all zeros of the function $f ( x ) = ( x + 6 ) ( x + 3 i ) ( x - 3 i )$ .

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

Find a polynomial function of the lowest degree with real coefficients that has the zeros below and whose leading coefficient is one. $0 , - 3,1 + 3 i$

Find real numbers $a$ and $b$ such that the equation $a + b i = - 10 + 10 i$ is true.

Compare the graph of $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ with $s ( x ) = x ^ { 2 }$ . $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ shifts right 5 units, shifts downward 9 units, and shrinks by a

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

Determine the $x$ -intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } - 10 x + 26$ .

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

Review of Graphs, Equations, and Inequalities

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Exam 2: Polynomial and Rational Functions

Find all real zeros of the polynomial f(x)=x4+13x3+40x2f ( x ) = x ^ { 4 } + 13 x ^ { 3 } + 40 x ^ { 2 }f(x)=x4+13x3+40x2 and determine the mutiplicity of each.

Match the equation with its graph. f(x)=x2+2x−3f ( x ) = x ^ { 2 } + 2 x - 3f(x)=x2+2x−3

Find the zeros of the function below algebraically, if any exist. f(x)=x5−5x3+4xf ( x ) = x ^ { 5 } - 5 x ^ { 3 } + 4 xf(x)=x5−5x3+4x

Write the complex conjugate of the following complex number and then multiply the number by the complex conjugate. Write the result in standard form. 2+−272 + \sqrt { - 27 }2+−27​

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 Absolute value of the leading coefficient is one

Use long division to divide. (x4−x2−5)÷(x2+4x−1)\left( x ^ { 4 } - x ^ { 2 } - 5 \right) \div \left( x ^ { 2 } + 4 x - 1 \right)(x4−x2−5)÷(x2+4x−1)

Identify any horizontal and vertical asymptotes of the function below. f(x)=2x−8∣x∣+6f ( x ) = \frac { 2 x - 8 } { | x | + 6 }f(x)=∣x∣+62x−8​

Determine the domain of f(x)=3x+3x2−3xf ( x ) = \frac { 3 x + 3 } { x ^ { 2 } - 3 x }f(x)=x2−3x3x+3​ .

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

Find two positive real numbers whose product is a maximum and whose sum of the first number and four times the second is 200 .

Simplify fff below and find any vertical asymptotes of fff . f(x)=x2−25x+5f ( x ) = \frac { x ^ { 2 } - 25 } { x + 5 }f(x)=x+5x2−25​

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:

Find the quadratic function fff whose graph intersects the xxx -axis at (2,0)( 2,0 )(2,0) and (3,0)( 3,0 )(3,0) and the yyy -axis at (0,−18)( 0 , - 18 )(0,−18) .

Find all zeros of the function f(x)=(x+6)(x+3i)(x−3i)f ( x ) = ( x + 6 ) ( x + 3 i ) ( x - 3 i )f(x)=(x+6)(x+3i)(x−3i) .

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

Find a polynomial function of the lowest degree with real coefficients that has the zeros below and whose leading coefficient is one. 0,−3,1+3i0 , - 3,1 + 3 i0,−3,1+3i

Find real numbers aaa and bbb such that the equation a+bi=−10+10ia + b i = - 10 + 10 ia+bi=−10+10i is true.

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 . s(x)=5(x−5)2+9s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9s(x)=5(x−5)2+9 shifts right 5 units, shifts downward 9 units, and shrinks by a

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 .

Determine the xxx -intercept(s) of the quadratic function f(x)=x2−10x+26f ( x ) = x ^ { 2 } - 10 x + 26f(x)=x2−10x+26 .

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

Review of Graphs, Equations, and Inequalities

Filters

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 13 x ^ { 3 } + 40 x ^ { 2 }$ and determine the mutiplicity of each.

Match the equation with its graph. $f ( x ) = x ^ { 2 } + 2 x - 3$

Find the zeros of the function below algebraically, if any exist. $f ( x ) = x ^ { 5 } - 5 x ^ { 3 } + 4 x$

Write the complex conjugate of the following complex number and then multiply the number by the complex conjugate. Write the result in standard form. $2 + \sqrt { - 27 }$

Use long division to divide. $\left( x ^ { 4 } - x ^ { 2 } - 5 \right) \div \left( x ^ { 2 } + 4 x - 1 \right)$

Identify any horizontal and vertical asymptotes of the function below. $f ( x ) = \frac { 2 x - 8 } { | x | + 6 }$

Determine the domain of $f ( x ) = \frac { 3 x + 3 } { x ^ { 2 } - 3 x }$ .

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

Simplify $f$ below and find any vertical asymptotes of $f$ . $f ( x ) = \frac { x ^ { 2 } - 25 } { x + 5 }$

Find the quadratic function $f$ whose graph intersects the $x$ -axis at $( 2,0 )$ and $( 3,0 )$ and the $y$ -axis at $( 0 , - 18 )$ .

Find all zeros of the function $f ( x ) = ( x + 6 ) ( x + 3 i ) ( x - 3 i )$ .

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

Find a polynomial function of the lowest degree with real coefficients that has the zeros below and whose leading coefficient is one. $0 , - 3,1 + 3 i$

Find real numbers $a$ and $b$ such that the equation $a + b i = - 10 + 10 i$ is true.

Compare the graph of $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ with $s ( x ) = x ^ { 2 }$ . $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ shifts right 5 units, shifts downward 9 units, and shrinks by a

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

Determine the $x$ -intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } - 10 x + 26$ .