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)  $\frac { 27 } { 8 } + \frac { 83 } { 8 } i$

Question 2

Determine the zeros (if any) of the rational function $g ( x ) = 7 + \frac { 3 } { x ^ { 2 } + 7 }$.

Accepted Answer

A)  $x = - \sqrt { 7 } , x = \sqrt { 7 }$ 
B)  $x = - 3$ 
C)  $x = - \frac { 3 } { 7 } , x = \frac { 3 } { 7 }$ 
D)  $x = - 7 , x = 7$ 
E)  no zeros 
A)  $x = - \sqrt { 7 } , x = \sqrt { 7 }$ 
B)  $x = - 3$ 
C)  $x = - \frac { 3 } { 7 } , x = \frac { 3 } { 7 }$ 
D)  $x = - 7 , x = 7$ 
E)  no zeros

Question 3

Find a fifth degree polynomial function of the lowest degree that has the zeros below and whose leading coefficient is one. $- 4 , - 1,0,1,4$

Accepted Answer

A)  $f ( x ) = x ^ { 5 } + 4 x ^ { 4 } - 13 x ^ { 3 } + 27 x ^ { 2 } + 36 x$ 
B)  $f ( x ) = x ^ { 5 } + 4 x ^ { 4 } - 13 x ^ { 3 } - 27 x ^ { 2 } + 36 x$ 
C)  $f ( x ) = x ^ { 5 } + 5 x ^ { 4 } - 19 x ^ { 3 } - 16 x ^ { 2 } + 48 x$ 
D)  $f ( x ) = x ^ { 5 } + 7 x ^ { 4 } - 13 x ^ { 3 } - x ^ { 2 } + 12 x$ 
E)  $f ( x ) = x ^ { 5 } - 17 x ^ { 3 } + 16 x$ 
A)  $f ( x ) = x ^ { 5 } + 4 x ^ { 4 } - 13 x ^ { 3 } + 27 x ^ { 2 } + 36 x$ 
B)  $f ( x ) = x ^ { 5 } + 4 x ^ { 4 } - 13 x ^ { 3 } - 27 x ^ { 2 } + 36 x$ 
C)  $f ( x ) = x ^ { 5 } + 5 x ^ { 4 } - 19 x ^ { 3 } - 16 x ^ { 2 } + 48 x$ 
D)  $f ( x ) = x ^ { 5 } + 7 x ^ { 4 } - 13 x ^ { 3 } - x ^ { 2 } + 12 x$ 
E)  $f ( x ) = x ^ { 5 } - 17 x ^ { 3 } + 16 x$

Question 4

A polynomial function $f$ has degree 3 , the zeros below, and a solution point of $f ( 1 ) = - 96$. Write $f$ in completely factored form.
$- 2 , - 3 + 4 i$

Accepted Answer

A)  $f ( x ) = ( x + 3 ) ( x + 2 - 4 i ) ( x + 2 + 4 i )$ 
B)  $f ( x ) = - ( x + 2 ) ( x - 4 - 3 i ) ( x - 4 + 3 i )$ 
C)  $f ( x ) = ( x + 2 ) ( x - 4 - 3 i ) ( x - 4 + 3 i )$ 
D)  $f ( x ) = - ( x + 2 ) ( x + 3 - 4 i ) ( x + 3 + 4 i )$ 
E)  $f ( x ) = ( x + 2 ) ( x + 3 - 4 i ) ( x + 3 + 4 i )$ 
A)  $f ( x ) = ( x + 3 ) ( x + 2 - 4 i ) ( x + 2 + 4 i )$ 
B)  $f ( x ) = - ( x + 2 ) ( x - 4 - 3 i ) ( x - 4 + 3 i )$ 
C)  $f ( x ) = ( x + 2 ) ( x - 4 - 3 i ) ( x - 4 + 3 i )$ 
D)  $f ( x ) = - ( x + 2 ) ( x + 3 - 4 i ) ( x + 3 + 4 i )$ 
E)  $f ( x ) = ( x + 2 ) ( x + 3 - 4 i ) ( x + 3 + 4 i )$

Question 5

Determine the value that $f ( x ) = \frac { 4 x - 6 } { x ^ { 2 } - 7 }$ approaches as $x$ increases and decreases in magnitude without bound.

Accepted Answer

A)  8 
B)  6 
C)  4 
D)  2 
E)  0 
A)  8 
B)  6 
C)  4 
D)  2 
E)  0

Question 6

Determine the $x$-intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } - 12 x + 37$.

Accepted Answer

A)  $( 1,0 ) , ( 9,0 )$ 
B)  $( 6,0 ) , ( 15,0 )$ 
C)  $( 8,0 ) , ( 3,0 )$ 
D)  $( 1,0 ) , ( 3,0 )$ 
E)  no $x$-intercept(s) 
A)  $( 1,0 ) , ( 9,0 )$ 
B)  $( 6,0 ) , ( 15,0 )$ 
C)  $( 8,0 ) , ( 3,0 )$ 
D)  $( 1,0 ) , ( 3,0 )$ 
E)  no $x$-intercept(s)

Question 7

Simplify $\frac { 4 + 3 i } { 5 + 2 i }$ and write the answer in standard form.

Accepted Answer

A)  $- \frac { 26 } { 29 } + \frac { 7 } { 29 } i$ 
B)  $\frac { 26 } { 29 } - \frac { 7 } { 29 } i$ 
C)  $\frac { 26 } { 29 } + \frac { 7 } { 29 } i$ 
D)  $\frac { 7 } { 29 } + \frac { 26 } { 29 } i$ 
E)  $\frac { 7 } { 29 } - \frac { 26 } { 29 } i$ 
A)  $- \frac { 26 } { 29 } + \frac { 7 } { 29 } i$ 
B)  $\frac { 26 } { 29 } - \frac { 7 } { 29 } i$ 
C)  $\frac { 26 } { 29 } + \frac { 7 } { 29 } i$ 
D)  $\frac { 7 } { 29 } + \frac { 26 } { 29 } i$ 
E)  $\frac { 7 } { 29 } - \frac { 26 } { 29 } i$

Question 8

Determine the vertex of the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }$.

Accepted Answer

A)  $\left( \frac { - 5 } { 2 } , \frac { 27 } { 2 } \right)$ 
B)  $\left( 5 , \frac { 29 } { 4 } \right)$ 
C)  $\left( \frac { 5 } { 2 } , \frac { 29 } { 4 } \right)$ 
D)  $\left( \frac { 5 } { 4 } , \frac { 21 } { 4 } \right)$ 
E)  $\left( \frac { - 5 } { 2 } , 1 \right)$ 
A)  $\left( \frac { - 5 } { 2 } , \frac { 27 } { 2 } \right)$ 
B)  $\left( 5 , \frac { 29 } { 4 } \right)$ 
C)  $\left( \frac { 5 } { 2 } , \frac { 29 } { 4 } \right)$ 
D)  $\left( \frac { 5 } { 4 } , \frac { 21 } { 4 } \right)$ 
E)  $\left( \frac { - 5 } { 2 } , 1 \right)$

Question 9

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 10

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

Question 11

Determine the vertex of the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5$.

Accepted Answer

A)  $( 0 , - 5 )$ 
B)  $( 5,0 )$ 
C)  $( 5,5 )$ 
D)  $( 0,5 )$ 
E)  $( - 5,0 )$ 
A)  $( 0 , - 5 )$ 
B)  $( 5,0 )$ 
C)  $( 5,5 )$ 
D)  $( 0,5 )$ 
E)  $( - 5,0 )$

Question 12

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)

Question 13

Use long division to divide.
$$\left( 6 x ^ { 2 } - 20 x + 6 \right) \div ( x - 3 )$$

Accepted Answer

A) $6 x - 38 + \frac { 120 } { x - 3 }$ 
B)  $6 x - 2$ 
C)  $6 x - 38 + \frac { 40 } { x - 3 }$ 
D)  $6 x - 40$ 
E)  $- 6 x + 2$ 
A) $6 x - 38 + \frac { 120 } { x - 3 }$ 
B)  $6 x - 2$ 
C)  $6 x - 38 + \frac { 40 } { x - 3 }$ 
D)  $6 x - 40$ 
E)  $- 6 x + 2$

Question 14

Find the zeros of the function below algebraically, if any exist.
$$f ( x ) = x ^ { 4 } + 8 x ^ { 2 } + 15$$

Accepted Answer

A)  $- \sqrt { 5 } , - \sqrt { 3 } , \sqrt { 3 }$, and $\sqrt { 5 }$ 
B)  $- \sqrt { 3 } , 0$, and $\sqrt { 3 }$ 
C)  $- \sqrt { 3 }$ and $\sqrt { 3 }$ 
D)  $- \sqrt { 5 }$ and $\sqrt { 5 }$ 
E)  No zeros exist. 
A)  $- \sqrt { 5 } , - \sqrt { 3 } , \sqrt { 3 }$, and $\sqrt { 5 }$ 
B)  $- \sqrt { 3 } , 0$, and $\sqrt { 3 }$ 
C)  $- \sqrt { 3 }$ and $\sqrt { 3 }$ 
D)  $- \sqrt { 5 }$ and $\sqrt { 5 }$ 
E)  No zeros exist.

Question 15

Find real numbers $a$ and $b$ such that the equation $a + b i = 10 - 12 i$ is true.

Accepted Answer

A)  $a = - 10 , b = 12$ 
B)  $\quad a = 10 , b = 12$ 
C)  $\quad a = - 10 , b = - 12$ 
D)  $\quad a = 10 , b = - 12$ 
E)  $\quad a = 22 , b = - 2$ 
A)  $a = - 10 , b = 12$ 
B)  $\quad a = 10 , b = 12$ 
C)  $\quad a = - 10 , b = - 12$ 
D)  $\quad a = 10 , b = - 12$ 
E)  $\quad a = 22 , b = - 2$

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 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 17

Find a polynomial function of the lowest degree with real coefficients that has the zeros below and whose leading coefficient is one. $0,2,4 - i$

Accepted Answer

A)  $f ( x ) = x ^ { 4 } - 34 x ^ { 3 } + 32 x ^ { 2 } - 10 x$ 
B)  $f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 33 x ^ { 2 } - 34 x$ 
C)  $f ( x ) = x ^ { 4 } + 32 x ^ { 3 } - 10 x ^ { 2 } - 34 x$ 
D)  $f ( x ) = x ^ { 4 } - 10 x ^ { 3 } - 34 x ^ { 2 } + 32 x$ 
E)  $f ( x ) = x ^ { 4 } + 32 x ^ { 3 } - 34 x ^ { 2 } - 10 x$ 
A)  $f ( x ) = x ^ { 4 } - 34 x ^ { 3 } + 32 x ^ { 2 } - 10 x$ 
B)  $f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 33 x ^ { 2 } - 34 x$ 
C)  $f ( x ) = x ^ { 4 } + 32 x ^ { 3 } - 10 x ^ { 2 } - 34 x$ 
D)  $f ( x ) = x ^ { 4 } - 10 x ^ { 3 } - 34 x ^ { 2 } + 32 x$ 
E)  $f ( x ) = x ^ { 4 } + 32 x ^ { 3 } - 34 x ^ { 2 } - 10 x$

Question 18

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 .

Question 19

Use the regression feature of a graphing utility to find a quadratic model for the data below. 
$\begin{array}{|r|c|}
\hline \boldsymbol{x} & \boldsymbol{y} \
\hline-2 & 9.8 \
\hline-1 & 4.1 \
\hline 0 & 3.3 \
\hline 1 & 6.6 \
\hline 2 & 13.8 \
\hline 3 & 24.1 \
\hline 4 & 39.5 \
\hline
\end{array}$

Accepted Answer

A)  $y = 1.91 x ^ { 2 } + 1.06 x + 3.15$ 
B)  $y = 1.81 x ^ { 2 } + 1.02 x + 3.3$ 
C)  $y = 2.21 x ^ { 2 } + 0.92 x + 3.3$ 
D)  $y = 2.11 x ^ { 2 } + 0.87 x + 3.65$ 
E)  $y = 2.01 x ^ { 2 } + 0.97 x + 3.44$ 
A)  $y = 1.91 x ^ { 2 } + 1.06 x + 3.15$ 
B)  $y = 1.81 x ^ { 2 } + 1.02 x + 3.3$ 
C)  $y = 2.21 x ^ { 2 } + 0.92 x + 3.3$ 
D)  $y = 2.11 x ^ { 2 } + 0.87 x + 3.65$ 
E)  $y = 2.01 x ^ { 2 } + 0.97 x + 3.44$

Question 20

Write $f ( x ) = x ^ { 3 } - 11 x ^ { 2 } + 18 x + 25$ in the form $f ( x ) = ( x - k ) q ( x ) + r$ when $k = 6 + \sqrt { 6 }$.

Accepted Answer

A)  $f ( x ) = [ x + ( 6 + \sqrt { 6 } ) ] \left[ x ^ { 2 } + ( - 5 + \sqrt { 6 } ) x - ( 6 - \sqrt { 6 } ) \right] - 5$ 
B)  $f ( x ) = [ x + ( 6 + \sqrt { 6 } ) ] \left[ x ^ { 2 } + ( - 5 + \sqrt { 6 } ) x - ( 6 - \sqrt { 6 } ) \right] + 5$ 
C)  $f ( x ) = [ x - ( 6 + \sqrt { 6 } ) ] \left[ x ^ { 2 } + ( - 5 + \sqrt { 6 } ) x - ( 6 - \sqrt { 6 } ) \right] + 5$ 
D)  $f ( x ) = [ x - ( 6 + \sqrt { 6 } ) ] \left[ x ^ { 2 } + ( - 5 + \sqrt { 6 } ) x - ( 6 - \sqrt { 6 } ) \right] - 5$ 
E)  $f ( x ) = [ x + ( 6 + \sqrt { 6 } ) ] \left[ x ^ { 2 } - ( - 5 + \sqrt { 6 } ) x - ( 6 - \sqrt { 6 } ) \right] - 5$ 
A)  $f ( x ) = [ x + ( 6 + \sqrt { 6 } ) ] \left[ x ^ { 2 } + ( - 5 + \sqrt { 6 } ) x - ( 6 - \sqrt { 6 } ) \right] - 5$ 
B)  $f ( x ) = [ x + ( 6 + \sqrt { 6 } ) ] \left[ x ^ { 2 } + ( - 5 + \sqrt { 6 } ) x - ( 6 - \sqrt { 6 } ) \right] + 5$ 
C)  $f ( x ) = [ x - ( 6 + \sqrt { 6 } ) ] \left[ x ^ { 2 } + ( - 5 + \sqrt { 6 } ) x - ( 6 - \sqrt { 6 } ) \right] + 5$ 
D)  $f ( x ) = [ x - ( 6 + \sqrt { 6 } ) ] \left[ x ^ { 2 } + ( - 5 + \sqrt { 6 } ) x - ( 6 - \sqrt { 6 } ) \right] - 5$ 
E)  $f ( x ) = [ x + ( 6 + \sqrt { 6 } ) ] \left[ x ^ { 2 } - ( - 5 + \sqrt { 6 } ) x - ( 6 - \sqrt { 6 } ) \right] - 5$

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

Determine the zeros (if any) of the rational function $g ( x ) = 7 + \frac { 3 } { x ^ { 2 } + 7 }$ .

Find a fifth degree polynomial function of the lowest degree that has the zeros below and whose leading coefficient is one. $- 4 , - 1,0,1,4$

A polynomial function $f$ has degree 3 , the zeros below, and a solution point of $f ( 1 ) = - 96$ . Write $f$ in completely factored form. $- 2 , - 3 + 4 i$

Determine the value that $f ( x ) = \frac { 4 x - 6 } { x ^ { 2 } - 7 }$ approaches as $x$ increases and decreases in magnitude without bound.

Determine the $x$ -intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } - 12 x + 37$ .

Simplify $\frac { 4 + 3 i } { 5 + 2 i }$ and write the answer in standard form.

Determine the vertex of the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }$ .

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

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

Determine the vertex of the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5$ .

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

Use long division to divide. $\left( 6 x ^ { 2 } - 20 x + 6 \right) \div ( x - 3 )$

Find the zeros of the function below algebraically, if any exist. $f ( x ) = x ^ { 4 } + 8 x ^ { 2 } + 15$

Find real numbers $a$ and $b$ such that the equation $a + b i = 10 - 12 i$ is true.

Find a polynomial function of the lowest degree with real coefficients that has the zeros below and whose leading coefficient is one. $0,2,4 - i$

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

Use the regression feature of a graphing utility to find a quadratic model for the data below. -2 9.8 -1 4.1 0 3.3 1 6.6 2 13.8 3 24.1 4 39.5

Write $f ( x ) = x ^ { 3 } - 11 x ^ { 2 } + 18 x + 25$ in the form $f ( x ) = ( x - k ) q ( x ) + r$ when $k = 6 + \sqrt { 6 }$ .

Functions and Their Graphs

Exponential and Logarithmic Functions

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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 zeros (if any) of the rational function g(x)=7+3x2+7g ( x ) = 7 + \frac { 3 } { x ^ { 2 } + 7 }g(x)=7+x2+73​ .

Find a fifth degree polynomial function of the lowest degree that has the zeros below and whose leading coefficient is one. −4,−1,0,1,4- 4 , - 1,0,1,4−4,−1,0,1,4

A polynomial function fff has degree 3 , the zeros below, and a solution point of f(1)=−96f ( 1 ) = - 96f(1)=−96 . Write fff in completely factored form. −2,−3+4i- 2 , - 3 + 4 i−2,−3+4i

Determine the value that f(x)=4x−6x2−7f ( x ) = \frac { 4 x - 6 } { x ^ { 2 } - 7 }f(x)=x2−74x−6​ approaches as xxx increases and decreases in magnitude without bound.

Determine the xxx -intercept(s) of the quadratic function f(x)=x2−12x+37f ( x ) = x ^ { 2 } - 12 x + 37f(x)=x2−12x+37 .

Simplify 4+3i5+2i\frac { 4 + 3 i } { 5 + 2 i }5+2i4+3i​ and write the answer in standard form.

Determine the vertex of the graph of the quadratic function f(x)=x2+5x+294f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }f(x)=x2+5x+429​ .

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.

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

Determine the vertex of the graph of the quadratic function f(x)=x2+5f ( x ) = x ^ { 2 } + 5f(x)=x2+5 .

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

Use long division to divide. (6x2−20x+6)÷(x−3)\left( 6 x ^ { 2 } - 20 x + 6 \right) \div ( x - 3 )(6x2−20x+6)÷(x−3)

Find the zeros of the function below algebraically, if any exist. f(x)=x4+8x2+15f ( x ) = x ^ { 4 } + 8 x ^ { 2 } + 15f(x)=x4+8x2+15

Find real numbers aaa and bbb such that the equation a+bi=10−12ia + b i = 10 - 12 ia+bi=10−12i is true.

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 a polynomial function of the lowest degree with real coefficients that has the zeros below and whose leading coefficient is one. 0,2,4−i0,2,4 - i0,2,4−i

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 .

Use the regression feature of a graphing utility to find a quadratic model for the data below. -2 9.8 -1 4.1 0 3.3 1 6.6 2 13.8 3 24.1 4 39.5

Write f(x)=x3−11x2+18x+25f ( x ) = x ^ { 3 } - 11 x ^ { 2 } + 18 x + 25f(x)=x3−11x2+18x+25 in the form f(x)=(x−k)q(x)+rf ( x ) = ( x - k ) q ( x ) + rf(x)=(x−k)q(x)+r when k=6+6k = 6 + \sqrt { 6 }k=6+6​ .

Functions and Their Graphs

Exponential and Logarithmic Functions

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Calculus Practice Problems

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

Determine the zeros (if any) of the rational function $g ( x ) = 7 + \frac { 3 } { x ^ { 2 } + 7 }$ .

Find a fifth degree polynomial function of the lowest degree that has the zeros below and whose leading coefficient is one. $- 4 , - 1,0,1,4$

A polynomial function $f$ has degree 3 , the zeros below, and a solution point of $f ( 1 ) = - 96$ . Write $f$ in completely factored form. $- 2 , - 3 + 4 i$

Determine the value that $f ( x ) = \frac { 4 x - 6 } { x ^ { 2 } - 7 }$ approaches as $x$ increases and decreases in magnitude without bound.

Determine the $x$ -intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } - 12 x + 37$ .

Simplify $\frac { 4 + 3 i } { 5 + 2 i }$ and write the answer in standard form.

Determine the vertex of the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }$ .

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

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

Determine the vertex of the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5$ .

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

Use long division to divide. $\left( 6 x ^ { 2 } - 20 x + 6 \right) \div ( x - 3 )$

Find the zeros of the function below algebraically, if any exist. $f ( x ) = x ^ { 4 } + 8 x ^ { 2 } + 15$

Find real numbers $a$ and $b$ such that the equation $a + b i = 10 - 12 i$ is true.

Find a polynomial function of the lowest degree with real coefficients that has the zeros below and whose leading coefficient is one. $0,2,4 - i$

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

Write $f ( x ) = x ^ { 3 } - 11 x ^ { 2 } + 18 x + 25$ in the form $f ( x ) = ( x - k ) q ( x ) + r$ when $k = 6 + \sqrt { 6 }$ .