Question 1

Provide an appropriate response.
-What is the range of the graph?

Accepted Answer

A)  $( - 8.85,44.86 )$ 
B)  $( - \infty , \infty )$ 
C)  $( - 3.43,8.61 )$ 
D)  $( - 8.85 , \infty )$ 
A)  $( - 8.85,44.86 )$ 
B)  $( - \infty , \infty )$ 
C)  $( - 3.43,8.61 )$ 
D)  $( - 8.85 , \infty )$

Question 2

Determine whether the statement is true or false.
-$$\text { If } \mathrm { c } \text { and } d \text { are complex numbers, then } \overline { c - d } = \bar { c } - \bar { d }$$

Accepted Answer

A) True 
 B)False

Question 3

Solve the inequality. Write the solution set in interval notation.
-$- x ^ { 2 } + 6 x - 4 \geq 0$

Accepted Answer

A)  $( \infty , - 3 - \sqrt { 5 } ] \cup [ - 3 + \sqrt { 5 } , \infty )$ 
B)  $( \infty , 3 - \sqrt { 5 } ] \cup [ 3 + \sqrt { 5 } , \infty )$ 
C)  $[ - 3 - \sqrt { 5 } , - 3 + \sqrt { 5 } ]$ 
D)  $[ 3 - \sqrt { 5 } , 3 + \sqrt { 5 } ]$ 
A)  $( \infty , - 3 - \sqrt { 5 } ] \cup [ - 3 + \sqrt { 5 } , \infty )$ 
B)  $( \infty , 3 - \sqrt { 5 } ] \cup [ 3 + \sqrt { 5 } , \infty )$ 
C)  $[ - 3 - \sqrt { 5 } , - 3 + \sqrt { 5 } ]$ 
D)  $[ 3 - \sqrt { 5 } , 3 + \sqrt { 5 } ]$

Question 4

Translate the given formula to an English phrase using the word "varies".
-If y varies inversely as x, and x is halved, how is y changed?

Accepted Answer

A)  y is doubled 
B)  y is decreased by 2 
C)  y is unchanged 
D)  y is halved 
A)  y is doubled 
B)  y is decreased by 2 
C)  y is unchanged 
D)  y is halved

Question 5

Round your answer to two decimal places.
-The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 2.25 lb when the masses are 4 ft apart, what is the attraction
When the masses are 6 ft apart?

Accepted Answer

A)  3 lb 
B)  2 lb 
C)  4 lb 
D)  1 lb 
A)  3 lb 
B)  2 lb 
C)  4 lb 
D)  1 lb

Question 6

Find a polynomial of least degree with only real coefficients and having the given zeros.
-$2 - i , - 6$

Accepted Answer

A)  $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 19 x + 30$ 
B)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 19 x + 24$ 
C)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 19 x - 30$ 
D)  $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - 20 x + 30$ 
A)  $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 19 x + 30$ 
B)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 19 x + 24$ 
C)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 19 x - 30$ 
D)  $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - 20 x + 30$

Question 7

Use synthetic division to decide whether the given number k is a zero of the given polynomial function.
-$k = 5 i ; f ( x ) = x ^ { 3 } + 3 x ^ { 2 } + 25 x + 75$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 8

Solve the problem
-A farmer has 400 feet of fence with which to fence a rectangular plot of land. The plot lies along a river so that only three sides need to be fenced. Estimate the largest area that can be fenced.

Accepted Answer

A)  $16,000 \mathrm { ft } ^ { 2 }$ 
B)  $20,000 \mathrm { ft } ^ { 2 }$ 
C)  $30,000 \mathrm { ft } ^ { 2 }$ 
D)  $24,000 \mathrm { ft } ^ { 2 }$ 
A)  $16,000 \mathrm { ft } ^ { 2 }$ 
B)  $20,000 \mathrm { ft } ^ { 2 }$ 
C)  $30,000 \mathrm { ft } ^ { 2 }$ 
D)  $24,000 \mathrm { ft } ^ { 2 }$

Question 9

Graph the function.
-$$f ( x ) = \frac { 10 } { x ^ { 2 } } - 4$$

Accepted Answer

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

Question 10

Match the equation to the correct graph.
-$$y = ( x - 1 ) ^ { 2 }$$

Accepted Answer

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

Question 11

Use synthetic division to perform the division.
-$$\frac { x ^ { 3 } - 1 } { x - 1 }$$

Accepted Answer

A)  $x ^ { 2 } + x + 1 + \frac { 1 } { x - 1 }$ 
B)  $x ^ { 3 } + x ^ { 2 } + x + 1 + \frac { 1 } { x - 1 }$ 
C)  $x ^ { 2 } + x + 1$ 
D)  $x ^ { 3 } + x ^ { 2 } + x + 1$ 
A)  $x ^ { 2 } + x + 1 + \frac { 1 } { x - 1 }$ 
B)  $x ^ { 3 } + x ^ { 2 } + x + 1 + \frac { 1 } { x - 1 }$ 
C)  $x ^ { 2 } + x + 1$ 
D)  $x ^ { 3 } + x ^ { 2 } + x + 1$

Question 12

Round your answer to two decimal places.
-The weight W of an object on the Moon varies directly as the weight E on earth. A person who weighs 192 lb on earth weighs 38.4 lb on the Moon. How much would a 104-lb person weigh on The Moon?

Accepted Answer

A)  520 lb 
B)  334.4 lb 
C)  .2 lb 
D)  20.8 lb 
A)  520 lb 
B)  334.4 lb 
C)  .2 lb 
D)  20.8 lb

Question 13

Solve the inequality. Write the solution set in interval notation.
-$$- x ^ { 2 } + 8 x - 14 < 0$$

Accepted Answer

A)  $( - 4 - \sqrt { 2 } , - 4 + \sqrt { 2 } )$ 
B)  $( \infty , - 4 - \sqrt { 2 } ) \cup ( - 4 + \sqrt { 2 } , \infty )$ 
C)  $( 4 - \sqrt { 2 } , 4 + \sqrt { 2 } )$ 
D)  $( \infty , 4 - \sqrt { 2 } ) \cup ( 4 + \sqrt { 2 } , \infty )$ 
A)  $( - 4 - \sqrt { 2 } , - 4 + \sqrt { 2 } )$ 
B)  $( \infty , - 4 - \sqrt { 2 } ) \cup ( - 4 + \sqrt { 2 } , \infty )$ 
C)  $( 4 - \sqrt { 2 } , 4 + \sqrt { 2 } )$ 
D)  $( \infty , 4 - \sqrt { 2 } ) \cup ( 4 + \sqrt { 2 } , \infty )$

Question 14

Solve the problem
-A piece of cardboard is twice as long as it is wide. It is to be made into a box with an open top by cutting 4 cm squares from each corner and folding up the sides. Let x represent the width of the
Original piece of cardboard. Determine a function V that represents the volume of the box in terms
Of x.

Accepted Answer

A)  $V ( x ) = 8 x ^ { 2 }$ 
B)  $V ( x ) = 8 x ^ { 2 } - 96 x + 256$ 
C)  $V ( x ) = 4 x ^ { 2 } - 64 x + 256$ 
D)  $V ( x ) = 8 x ^ { 2 } - 48 x + 64$ 
A)  $V ( x ) = 8 x ^ { 2 }$ 
B)  $V ( x ) = 8 x ^ { 2 } - 96 x + 256$ 
C)  $V ( x ) = 4 x ^ { 2 } - 64 x + 256$ 
D)  $V ( x ) = 8 x ^ { 2 } - 48 x + 64$

Question 15

Give the equations of any horizontal asymptotes.
-$$g ( x ) = \frac { x ^ { 2 } + 8 x - 5 } { x - 5 }$$

Accepted Answer

A)  none 
B)  $y = - 5$ 
C)  $y = 0$ 
D)  $y = 8$ 
A)  none 
B)  $y = - 5$ 
C)  $y = 0$ 
D)  $y = 8$

Question 16

For the polynomial, one zero is given. Find all others.
-$$P ( x ) = x ^ { 3 } - 8 x ^ { 2 } + 17 x - 30 ; 6$$

Accepted Answer

A)  $1 + 2 \mathrm { i } , 1 - 2 \mathrm { i }$ 
B)  $1 + \sqrt { 5 } \mathrm { i } , 1 - \sqrt { 5 } \mathrm { i }$ 
C)  $- 1 + 2 \mathrm { i } , - 1 - 2 \mathrm { i }$ 
D)  $1 + \sqrt { 5 } , 1 - \sqrt { 5 }$ 
A)  $1 + 2 \mathrm { i } , 1 - 2 \mathrm { i }$ 
B)  $1 + \sqrt { 5 } \mathrm { i } , 1 - \sqrt { 5 } \mathrm { i }$ 
C)  $- 1 + 2 \mathrm { i } , - 1 - 2 \mathrm { i }$ 
D)  $1 + \sqrt { 5 } , 1 - \sqrt { 5 }$

Question 17

Translate the given formula to an English phrase using the word "varies".
-$$\mathrm { A } = \pi \mathrm { r } ^ { 2 } \text {, where } \mathrm { A } \text { is the area of a circle of radius } \mathrm { r } \text {. }$$

Accepted Answer

The area of a circle

Question 18

Solve the inequality. Write the solution set in interval notation.
-$$2 x ^ { 2 } - 7 x \geq 15$$

Accepted Answer

A)  $( \infty , - 5 ] \cup \left[ \frac { 3 } { 2 } , \infty \right]$ 
B)  $\left[ - 5 , \frac { 3 } { 2 } \right]$ 
C)  $\left[ - \frac { 3 } { 2 } , 5 \right]$ 
D)  $\left( \infty , - \frac { 3 } { 2 } \right] \cup [ 5 , \infty )$ 
A)  $( \infty , - 5 ] \cup \left[ \frac { 3 } { 2 } , \infty \right]$ 
B)  $\left[ - 5 , \frac { 3 } { 2 } \right]$ 
C)  $\left[ - \frac { 3 } { 2 } , 5 \right]$ 
D)  $\left( \infty , - \frac { 3 } { 2 } \right] \cup [ 5 , \infty )$

Question 19

Factor f(x) into linear factors given that k is a zero of f(x).
-$$f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } - 5 x + 6 ; k = 1$$

Accepted Answer

A)  $( x + 1 ) ( x + 2 ) ( 2 x - 3 )$ 
B)  $( x - 1 ) ( x + 1 ) ( 2 x - 6 )$ 
C)  $( x - 1 ) ( x - 2 ) ( 2 x + 3 )$ 
D)  $( x - 1 ) ( x + 2 ) ( 2 x - 3 )$ 
A)  $( x + 1 ) ( x + 2 ) ( 2 x - 3 )$ 
B)  $( x - 1 ) ( x + 1 ) ( 2 x - 6 )$ 
C)  $( x - 1 ) ( x - 2 ) ( 2 x + 3 )$ 
D)  $( x - 1 ) ( x + 2 ) ( 2 x - 3 )$

Question 20

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zeros of $- 3,2,6$ and $P ( 1 ) = 20$

Accepted Answer

A)  $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 11 x + 30$ 
B)  $\mathrm { P } ( \mathrm { x } ) = \mathrm { x } ^ { 3 } + 5 \mathrm { x } ^ { 2 } - 11 \mathrm { x } + 30$ 
C)  $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 12 x - 36$ 
D)  $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 12 x + 36$ 
A)  $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 11 x + 30$ 
B)  $\mathrm { P } ( \mathrm { x } ) = \mathrm { x } ^ { 3 } + 5 \mathrm { x } ^ { 2 } - 11 \mathrm { x } + 30$ 
C)  $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 12 x - 36$ 
D)  $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 12 x + 36$

Provide an appropriate response. -What is the range of the graph?

Determine whether the statement is true or false. - $\text { If } \mathrm { c } \text { and } d \text { are complex numbers, then } \overline { c - d } = \bar { c } - \bar { d }$

Solve the inequality. Write the solution set in interval notation. - $- x ^ { 2 } + 6 x - 4 \geq 0$

Translate the given formula to an English phrase using the word "varies". -If y varies inversely as x, and x is halved, how is y changed?

Round your answer to two decimal places. -The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 2.25 lb when the masses are 4 ft apart, what is the attraction When the masses are 6 ft apart?

Find a polynomial of least degree with only real coefficients and having the given zeros. - $2 - i , - 6$

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = 5 i ; f ( x ) = x ^ { 3 } + 3 x ^ { 2 } + 25 x + 75$

Solve the problem -A farmer has 400 feet of fence with which to fence a rectangular plot of land. The plot lies along a river so that only three sides need to be fenced. Estimate the largest area that can be fenced.

Graph the function. - $f ( x ) = \frac { 10 } { x ^ { 2 } } - 4$ $Graph the function. - f ( x ) = \frac { 10 } { x ^ { 2 } } - 4$

Match the equation to the correct graph. - $y = ( x - 1 ) ^ { 2 }$

Use synthetic division to perform the division. - $\frac { x ^ { 3 } - 1 } { x - 1 }$

Round your answer to two decimal places. -The weight W of an object on the Moon varies directly as the weight E on earth. A person who weighs 192 lb on earth weighs 38.4 lb on the Moon. How much would a 104-lb person weigh on The Moon?

Solve the inequality. Write the solution set in interval notation. - $- x ^ { 2 } + 8 x - 14 < 0$

Give the equations of any horizontal asymptotes. - $g ( x ) = \frac { x ^ { 2 } + 8 x - 5 } { x - 5 }$

For the polynomial, one zero is given. Find all others. - $P ( x ) = x ^ { 3 } - 8 x ^ { 2 } + 17 x - 30 ; 6$

Translate the given formula to an English phrase using the word "varies". - $\mathrm { A } = \pi \mathrm { r } ^ { 2 } \text {, where } \mathrm { A } \text { is the area of a circle of radius } \mathrm { r } \text {. }$

Solve the inequality. Write the solution set in interval notation. - $2 x ^ { 2 } - 7 x \geq 15$

Factor f(x) into linear factors given that k is a zero of f(x). - $f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } - 5 x + 6 ; k = 1$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $- 3,2,6$ and $P ( 1 ) = 20$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 4: Polynomial and Rational Functions

Provide an appropriate response. -What is the range of the graph?

Determine whether the statement is true or false. - If c and d are complex numbers, then c−d‾=cˉ−dˉ\text { If } \mathrm { c } \text { and } d \text { are complex numbers, then } \overline { c - d } = \bar { c } - \bar { d } If c and d are complex numbers, then c−d​=cˉ−dˉ

Solve the inequality. Write the solution set in interval notation. - −x2+6x−4≥0- x ^ { 2 } + 6 x - 4 \geq 0−x2+6x−4≥0