Question 1

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

Accepted Answer

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

Question 2

Match the equation with its graph.
$$f ( x ) = \frac { x ^ { 4 } - 17 x ^ { 2 } + 16 } { 20 }$$

Accepted Answer

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

Question 3

Use long division to divide.
$$\left( x ^ { 3 } + 5 x ^ { 2 } + 36 x + 180 \right) \div ( x + 5 )$$

Accepted Answer

A)  $x ^ { 2 } + 30$ 
B)  $x ^ { 2 } + 10 x + 44 - \frac { 244 } { x + 5 }$ 
C)  $x ^ { 2 } + 10 x + 86 + \frac { 110 } { x + 5 }$ 
D)  $x ^ { 2 } + 10 x + 44$ 
E)  $x ^ { 2 } + 36$ 
A)  $x ^ { 2 } + 30$ 
B)  $x ^ { 2 } + 10 x + 44 - \frac { 244 } { x + 5 }$ 
C)  $x ^ { 2 } + 10 x + 86 + \frac { 110 } { x + 5 }$ 
D)  $x ^ { 2 } + 10 x + 44$ 
E)  $x ^ { 2 } + 36$

Question 4

Suppose the IQ scores $( y$, rounded to the nearest $10 )$ for a group of people are summarized in the table below. Use the regression feature of a graphing utility to find a quadratic function of the form $y = a x ^ { 2 } + b x + c$ for the data.
$\begin{array}{|c|c|}
\hline \text { IQ Score } & \text { Number of People } \
\boldsymbol{y} & \boldsymbol{x} \
\hline 70 & 50 \
\hline 80 & 76 \
\hline 90 & 89 \
\hline 100 & 93 \
\hline 110 & 74 \
\hline 120 & 53 \
\hline 130 & 16 \
\hline
\end{array}$

Accepted Answer

A)  $y = - 0.04 x ^ { 2 } + 15.08 x - 411.58$ 
B)  $y = - 0.06 x ^ { 2 } + 12.06 x - 484.21$ 
C)  $y = - 0.08 x ^ { 2 } + 10.98 x - 508.43$ 
D)  $y = - 0.07 x ^ { 2 } + 13.63 x - 460$ 
E)  $y = - 0.09 x ^ { 2 } + 8.56 x - 556.85$ 
A)  $y = - 0.04 x ^ { 2 } + 15.08 x - 411.58$ 
B)  $y = - 0.06 x ^ { 2 } + 12.06 x - 484.21$ 
C)  $y = - 0.08 x ^ { 2 } + 10.98 x - 508.43$ 
D)  $y = - 0.07 x ^ { 2 } + 13.63 x - 460$ 
E)  $y = - 0.09 x ^ { 2 } + 8.56 x - 556.85$

Question 5

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

Question 6

Write the standard form of the equation of the parabola that has a vertex at $\left( \frac { - 2 } { 3 } , \frac { 1 } { 9 } \right)$ and passes through the point $( 3 , - 4 )$.

Accepted Answer

A) 
$$f ( x ) = - \frac { 37 } { 11 } \left( x + \frac { 2 } { 3 } \right) ^ { 2 } + \frac { 1 } { 9 }$$ 
B) 
$$f ( x ) = - \frac { 37 } { 121 } \left( x - \frac { 3 } { 2 } \right) ^ { 2 } + \frac { 1 } { 9 }$$ 
C) 
$$f ( x ) = - \frac { 37 } { 121 } \left( x + \frac { 2 } { 3 } \right) ^ { 2 } + \frac { 1 } { 9 }$$ 
D) 
$$f ( x ) = - \frac { 37 } { 11 } \left( x - \frac { 2 } { 3 } \right) ^ { 2 } - \frac { 1 } { 9 }$$ 
E) 
$$f ( x ) = - \frac { 37 } { 25 } \left( x - \frac { 3 } { 2 } \right) ^ { 2 } - \frac { 1 } { 9 }$$ 
A) 
$$f ( x ) = - \frac { 37 } { 11 } \left( x + \frac { 2 } { 3 } \right) ^ { 2 } + \frac { 1 } { 9 }$$ 
B) 
$$f ( x ) = - \frac { 37 } { 121 } \left( x - \frac { 3 } { 2 } \right) ^ { 2 } + \frac { 1 } { 9 }$$ 
C) 
$$f ( x ) = - \frac { 37 } { 121 } \left( x + \frac { 2 } { 3 } \right) ^ { 2 } + \frac { 1 } { 9 }$$ 
D) 
$$f ( x ) = - \frac { 37 } { 11 } \left( x - \frac { 2 } { 3 } \right) ^ { 2 } - \frac { 1 } { 9 }$$ 
E) 
$$f ( x ) = - \frac { 37 } { 25 } \left( x - \frac { 3 } { 2 } \right) ^ { 2 } - \frac { 1 } { 9 }$$

Question 7

Perform the addition or subtraction and write the result in standard form.
$$- ( 7.2 - 12.3 i ) - ( 8.1 - \sqrt { - 1.21 } )$$

Accepted Answer

A)  $- 15.3 + 13.4 i$ 
B)  $0.9 + 13.4 i$ 
C)  $- 0.9 + 11.2 i$ 
D)  $- 15.3 + 11.2 i$ 
E)  $15.3 + 13.4 i$ 
A)  $- 15.3 + 13.4 i$ 
B)  $0.9 + 13.4 i$ 
C)  $- 0.9 + 11.2 i$ 
D)  $- 15.3 + 11.2 i$ 
E)  $15.3 + 13.4 i$

Question 8

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)  $\quad a = 4 , b = - 9$ 
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)  $\quad a = 4 , b = - 9$ 
E)  $\quad a = 13 , b = - 5$

Question 9

Simplify $\frac { 2 + 5 i } { 3 i }$ and write the answer in standard form.

Accepted Answer

A)  $- \frac { 5 } { 3 } - \frac { 2 i } { 3 }$ 
B)  $\frac { 5 } { 3 } - \frac { 2 i } { 3 }$ 
C)  $\frac { 5 } { 3 } + \frac { 2 i } { 3 }$ 
D)  $\frac { 2 } { 3 } + \frac { 5 i } { 3 }$ 
E)  $- \frac { 2 } { 3 } + \frac { 5 i } { 3 }$ 
A)  $- \frac { 5 } { 3 } - \frac { 2 i } { 3 }$ 
B)  $\frac { 5 } { 3 } - \frac { 2 i } { 3 }$ 
C)  $\frac { 5 } { 3 } + \frac { 2 i } { 3 }$ 
D)  $\frac { 2 } { 3 } + \frac { 5 i } { 3 }$ 
E)  $- \frac { 2 } { 3 } + \frac { 5 i } { 3 }$

Question 10

Use long division to divide.
$$\left( 2 x ^ { 2 } + 11 x + 12 \right) \div ( x + 4 )$$

Accepted Answer

A)  $2 x + 19 + \frac { 88 } { x + 4 }$ 
B)  $2 x + 3$ 
C)  $2 x + 19 + \frac { 22 } { x + 4 }$ 
D)  $2 x + 22$ 
E)  $- 2 x - 3$ 
A)  $2 x + 19 + \frac { 88 } { x + 4 }$ 
B)  $2 x + 3$ 
C)  $2 x + 19 + \frac { 22 } { x + 4 }$ 
D)  $2 x + 22$ 
E)  $- 2 x - 3$

Question 11

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 12

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

Accepted Answer

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

Question 13

Find two positive real numbers whose product is a maximum and whose sum is 146 .

Accepted Answer

A)  71,75 
B)  73,73 
C)  78,68 
D)  82,64 
E)  61,85 
A)  71,75 
B)  73,73 
C)  78,68 
D)  82,64 
E)  61,85

Question 14

If $x = \frac { 2 } { 5 }$ is a root of $25 x ^ { 3 } - 70 x ^ { 2 } + 44 x - 8 = 0$, use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Accepted Answer

A)  $( 5 x - 2 ) ( 5 x + 2 ) ( x - 2 ) ; x = \frac { 2 } { 5 } , - \frac { 2 } { 5 } , 2$ 
B)  $( 5 x + 2 ) ^ { 2 } ( x - 2 ) ; x = - \frac { 2 } { 5 } , 2$ 
C)  $( 5 x - 2 ) ( x - 2 ) ^ { 2 } ; x = \frac { 2 } { 5 } , 2$ 
D)  $( 5 x + 2 ) ( x - 2 ) ^ { 2 } ; x = - \frac { 2 } { 5 } , 2$ 
E)  $( 5 x - 2 ) ^ { 2 } ( x - 2 ) ; x = \frac { 2 } { 5 } , 2$ 
A)  $( 5 x - 2 ) ( 5 x + 2 ) ( x - 2 ) ; x = \frac { 2 } { 5 } , - \frac { 2 } { 5 } , 2$ 
B)  $( 5 x + 2 ) ^ { 2 } ( x - 2 ) ; x = - \frac { 2 } { 5 } , 2$ 
C)  $( 5 x - 2 ) ( x - 2 ) ^ { 2 } ; x = \frac { 2 } { 5 } , 2$ 
D)  $( 5 x + 2 ) ( x - 2 ) ^ { 2 } ; x = - \frac { 2 } { 5 } , 2$ 
E)  $( 5 x - 2 ) ^ { 2 } ( x - 2 ) ; x = \frac { 2 } { 5 } , 2$

Question 15

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 }$ and determine the mutiplicity of each.

Accepted Answer

A)  $x = 0$, multiplicity $2 ; x = - 2$, multiplicity $1 ; x = - 6$, multiplicity 1 
B)  $x = 2$, multiplicity $2 ; x = 6$, multiplicity 2 
C)  $x = 0$, multiplicity $2 ; x = 2$, multiplicity $1 ; x = 6$, multiplicity 1 
D)  $x = - 2$, multiplicity $2 ; x = - 6$, multiplicity 2 
E)  $x = 0$, multiplicity $1 ; x = 2$, multiplicity $1 ; x = - 2$, multiplicity $1 ; x = 6$, multiplicity 1 
A)  $x = 0$, multiplicity $2 ; x = - 2$, multiplicity $1 ; x = - 6$, multiplicity 1 
B)  $x = 2$, multiplicity $2 ; x = 6$, multiplicity 2 
C)  $x = 0$, multiplicity $2 ; x = 2$, multiplicity $1 ; x = 6$, multiplicity 1 
D)  $x = - 2$, multiplicity $2 ; x = - 6$, multiplicity 2 
E)  $x = 0$, multiplicity $1 ; x = 2$, multiplicity $1 ; x = - 2$, multiplicity $1 ; x = 6$, multiplicity 1

Question 16

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 17

Find the zeros of the function below algebraically, if any exist.
$$f ( x ) = x ^ { 5 } - 9 x ^ { 3 } + 27 x ^ { 2 } - 243$$

Accepted Answer

A)  $- 2$ and 2 
B)  $- 4$ and 2 
C)  $- 4$ and 4 
D)  $- 3$ and 4 
E)  $- 3$ and 3 
A)  $- 2$ and 2 
B)  $- 4$ and 2 
C)  $- 4$ and 4 
D)  $- 3$ and 4 
E)  $- 3$ and 3

Question 18

Find the zeros of the function below algebraically, if any exist. $$f ( x ) = x ^ { 6 } + 28 x ^ { 3 } + 27$$

Accepted Answer

A)  $- 3$ and $- 1$ 
B)  $- 2$ and $- 1$ 
C)  $- 3$ and $- 2$ 
D)  $- 2 , - 1,1$, and 2 
E)  $- 3 , - 2,2$, and 3 
A)  $- 3$ and $- 1$ 
B)  $- 2$ and $- 1$ 
C)  $- 3$ and $- 2$ 
D)  $- 2 , - 1,1$, and 2 
E)  $- 3 , - 2,2$, and 3

Question 19

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 20

Find the quadratic function $f$ whose graph intersects the $x$-axis at $( - 7,0 )$ and $( 1,0 )$ and the $y$-axis at $( 0 , - 14 )$.

Accepted Answer

A)  $f ( x ) = - 2 x ^ { 2 } - 16 x - 2$ 
B)  $f ( x ) = 2 x ^ { 2 } + 12 x - 14$ 
C)  $f ( x ) = 2 x ^ { 2 } + 16 x - 7$ 
D)  $f ( x ) = - 2 x ^ { 2 } + 16 x - 14$ 
E)  $f ( x ) = - 2 x ^ { 2 } - 12 x - 14$ 
A)  $f ( x ) = - 2 x ^ { 2 } - 16 x - 2$ 
B)  $f ( x ) = 2 x ^ { 2 } + 12 x - 14$ 
C)  $f ( x ) = 2 x ^ { 2 } + 16 x - 7$ 
D)  $f ( x ) = - 2 x ^ { 2 } + 16 x - 14$ 
E)  $f ( x ) = - 2 x ^ { 2 } - 12 x - 14$

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

Match the equation with its graph. $f ( x ) = \frac { x ^ { 4 } - 17 x ^ { 2 } + 16 } { 20 }$

Use long division to divide. $\left( x ^ { 3 } + 5 x ^ { 2 } + 36 x + 180 \right) \div ( x + 5 )$

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

Write the standard form of the equation of the parabola that has a vertex at $\left( \frac { - 2 } { 3 } , \frac { 1 } { 9 } \right)$ and passes through the point $( 3 , - 4 )$ .

Perform the addition or subtraction and write the result in standard form. $- ( 7.2 - 12.3 i ) - ( 8.1 - \sqrt { - 1.21 } )$

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

Simplify $\frac { 2 + 5 i } { 3 i }$ and write the answer in standard form.

Use long division to divide. $\left( 2 x ^ { 2 } + 11 x + 12 \right) \div ( x + 4 )$

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

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

Find two positive real numbers whose product is a maximum and whose sum is 146 .

If $x = \frac { 2 } { 5 }$ is a root of $25 x ^ { 3 } - 70 x ^ { 2 } + 44 x - 8 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 }$ and determine the mutiplicity of each.

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

Find the zeros of the function below algebraically, if any exist. $f ( x ) = x ^ { 5 } - 9 x ^ { 3 } + 27 x ^ { 2 } - 243$

Find the zeros of the function below algebraically, if any exist. $f ( x ) = x ^ { 6 } + 28 x ^ { 3 } + 27$

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

Find the quadratic function $f$ whose graph intersects the $x$ -axis at $( - 7,0 )$ and $( 1,0 )$ and the $y$ -axis at $( 0 , - 14 )$ .

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

Calculus Practice Problems

Filters

Exam 2: Polynomial and Rational Functions

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

Match the equation with its graph. f(x)=x4−17x2+1620f ( x ) = \frac { x ^ { 4 } - 17 x ^ { 2 } + 16 } { 20 }f(x)=20x4−17x2+16​

Use long division to divide. (x3+5x2+36x+180)÷(x+5)\left( x ^ { 3 } + 5 x ^ { 2 } + 36 x + 180 \right) \div ( x + 5 )(x3+5x2+36x+180)÷(x+5)

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​

Write the standard form of the equation of the parabola that has a vertex at (−23,19)\left( \frac { - 2 } { 3 } , \frac { 1 } { 9 } \right)(3−2​,91​) and passes through the point (3,−4)( 3 , - 4 )(3,−4) .

Perform the addition or subtraction and write the result in standard form. −(7.2−12.3i)−(8.1−−1.21)- ( 7.2 - 12.3 i ) - ( 8.1 - \sqrt { - 1.21 } )−(7.2−12.3i)−(8.1−−1.21​)

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

Simplify 2+5i3i\frac { 2 + 5 i } { 3 i }3i2+5i​ and write the answer in standard form.

Use long division to divide. (2x2+11x+12)÷(x+4)\left( 2 x ^ { 2 } + 11 x + 12 \right) \div ( x + 4 )(2x2+11x+12)÷(x+4)

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) .

Which of the following is the graph of the given equation? f(x)=2−xx+3f ( x ) = \frac { 2 - x } { x + 3 }f(x)=x+32−x​

Find two positive real numbers whose product is a maximum and whose sum is 146 .

If x=25x = \frac { 2 } { 5 }x=52​ is a root of 25x3−70x2+44x−8=025 x ^ { 3 } - 70 x ^ { 2 } + 44 x - 8 = 025x3−70x2+44x−8=0 , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Find all real zeros of the polynomial f(x)=x4+8x3+12x2f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 }f(x)=x4+8x3+12x2 and determine the mutiplicity of each.

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

Find the zeros of the function below algebraically, if any exist. f(x)=x5−9x3+27x2−243f ( x ) = x ^ { 5 } - 9 x ^ { 3 } + 27 x ^ { 2 } - 243f(x)=x5−9x3+27x2−243

Find the zeros of the function below algebraically, if any exist. f(x)=x6+28x3+27f ( x ) = x ^ { 6 } + 28 x ^ { 3 } + 27f(x)=x6+28x3+27

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 the quadratic function fff whose graph intersects the xxx -axis at (−7,0)( - 7,0 )(−7,0) and (1,0)( 1,0 )(1,0) and the yyy -axis at (0,−14)( 0 , - 14 )(0,−14) .

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

Calculus Practice Problems

Filters

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

Match the equation with its graph. $f ( x ) = \frac { x ^ { 4 } - 17 x ^ { 2 } + 16 } { 20 }$

Use long division to divide. $\left( x ^ { 3 } + 5 x ^ { 2 } + 36 x + 180 \right) \div ( x + 5 )$

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

Write the standard form of the equation of the parabola that has a vertex at $\left( \frac { - 2 } { 3 } , \frac { 1 } { 9 } \right)$ and passes through the point $( 3 , - 4 )$ .

Perform the addition or subtraction and write the result in standard form. $- ( 7.2 - 12.3 i ) - ( 8.1 - \sqrt { - 1.21 } )$

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

Simplify $\frac { 2 + 5 i } { 3 i }$ and write the answer in standard form.

Use long division to divide. $\left( 2 x ^ { 2 } + 11 x + 12 \right) \div ( x + 4 )$

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

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

If $x = \frac { 2 } { 5 }$ is a root of $25 x ^ { 3 } - 70 x ^ { 2 } + 44 x - 8 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 }$ and determine the mutiplicity of each.

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

Find the zeros of the function below algebraically, if any exist. $f ( x ) = x ^ { 5 } - 9 x ^ { 3 } + 27 x ^ { 2 } - 243$

Find the zeros of the function below algebraically, if any exist. $f ( x ) = x ^ { 6 } + 28 x ^ { 3 } + 27$

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

Find the quadratic function $f$ whose graph intersects the $x$ -axis at $( - 7,0 )$ and $( 1,0 )$ and the $y$ -axis at $( 0 , - 14 )$ .