Question 1

Use the remainder theorem and synthetic division to find f(k).
-$k = - 3 ; f ( x ) = 3 x ^ { 4 } + 5 x ^ { 3 } + 6 x ^ { 2 } - 6 x + 24$

Accepted Answer

A)  204 
B)  360 
C)  $- 444$ 
D)  282 
A)  204 
B)  360 
C)  $- 444$ 
D)  282

Question 2

Find all rational zeros and factor f(x).
-$$f ( x ) = x ^ { 3 } + 6 x ^ { 2 } - x - 6$$

Accepted Answer

A)  $1 , - 1,6 ; f ( x ) = ( x - 1 ) ( x + 1 ) ( x - 6 )$ 
B)  $1 , - 1 , - 6 ; f ( x ) = ( x - 1 ) ( x + 1 ) ( x$ 
C)  $1 , - 1 , - 7 ; f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 7 )$ 
D)  $1 , - 2,8 ; f ( x ) = ( x - 1 ) ( x + 2 ) ( x -$ 
A)  $1 , - 1,6 ; f ( x ) = ( x - 1 ) ( x + 1 ) ( x - 6 )$ 
B)  $1 , - 1 , - 6 ; f ( x ) = ( x - 1 ) ( x + 1 ) ( x$ 
C)  $1 , - 1 , - 7 ; f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 7 )$ 
D)  $1 , - 2,8 ; f ( x ) = ( x - 1 ) ( x + 2 ) ( x -$

Question 3

Find a polynomial of least degree with only real coefficients and having the given zeros.
-$3 + \sqrt { 2 } , 3 - \sqrt { 2 }$, and 2

Accepted Answer

A)  $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + 19 x - 14$ 
B)  $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 19 x + 14$ 
C)  $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 19 x + 16$ 
D)  $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } + 19 x - 14$ 
A)  $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + 19 x - 14$ 
B)  $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 19 x + 14$ 
C)  $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 19 x + 16$ 
D)  $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } + 19 x - 14$

Question 4

Solve the problem.
-In the following formula, $\mathrm { f } ( \mathrm { x } )$ is the minimum number of hours of studying required to attain a test score of $x : \quad f ( x ) = \frac { 0.41 x } { 100.5 - x }$. How many hours of study are needed to score 91 ?

Accepted Answer

A)  $9.62 \mathrm { hr }$ 
B)  $39.30 \mathrm { hr }$ 
C)  $3.93 \mathrm { hr }$ 
D)  $100.05 \mathrm { hr }$ 
A)  $9.62 \mathrm { hr }$ 
B)  $39.30 \mathrm { hr }$ 
C)  $3.93 \mathrm { hr }$ 
D)  $100.05 \mathrm { hr }$

Question 5

Find the domain and range of the function.
-$$f ( x ) = 3 x ^ { 2 } - 42 x + 151$$

Accepted Answer

A)  Domain: $( - \infty , \infty )$; Range: $[ 4 , \infty )$ 
B)  Domain: $( - \infty , \infty )$; Range: $[ 0 , \infty )$ 
C)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 0 ]$ 
D)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 7 ]$ 
A)  Domain: $( - \infty , \infty )$; Range: $[ 4 , \infty )$ 
B)  Domain: $( - \infty , \infty )$; Range: $[ 0 , \infty )$ 
C)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 0 ]$ 
D)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 7 ]$

Question 6

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

Question 7

Find all rational zeros and factor f(x).
-$$f ( x ) = 8 x ^ { 3 } + 2 x ^ { 2 } - 5 x + 1$$

Accepted Answer

A)  $2,4 , - 1 ; f ( x ) = ( 2 x - 1 ) ( 4 x - 1 ) ( x + 1 )$ 
B)  $\frac { 1 } { 2 } , \frac { 1 } { 4 } , - 1 ; f ( x ) = ( 2 x - 1 ) ( 4 x - 1 ) ( x + 1 )$ 
C)  $\frac { 1 } { 8 } , 4 , - 1 ; f ( x ) = ( 8 x - 1 ) ( x - 4 ) ( x + 1 )$ 
D)  $\frac { 1 } { 8 } , 1 , - 1 ; f ( x ) = ( 8 x - 1 ) ( x - 1 ) ( x + 1 )$ 
A)  $2,4 , - 1 ; f ( x ) = ( 2 x - 1 ) ( 4 x - 1 ) ( x + 1 )$ 
B)  $\frac { 1 } { 2 } , \frac { 1 } { 4 } , - 1 ; f ( x ) = ( 2 x - 1 ) ( 4 x - 1 ) ( x + 1 )$ 
C)  $\frac { 1 } { 8 } , 4 , - 1 ; f ( x ) = ( 8 x - 1 ) ( x - 4 ) ( x + 1 )$ 
D)  $\frac { 1 } { 8 } , 1 , - 1 ; f ( x ) = ( 8 x - 1 ) ( x - 1 ) ( x + 1 )$

Question 8

Find a polynomial of least degree with only real coefficients and having the given zeros.
-$4 + 2 i$ and $4 - 2 i$

Accepted Answer

A)  $x ^ { 2 } - 8 x + 12$ 
B)  $x ^ { 2 } + 8 x + 20$ 
C)  $x ^ { 2 } - 8 x + 20$ 
D)  $x ^ { 2 } + 20$ 
A)  $x ^ { 2 } - 8 x + 12$ 
B)  $x ^ { 2 } + 8 x + 20$ 
C)  $x ^ { 2 } - 8 x + 20$ 
D)  $x ^ { 2 } + 20$

Question 9

Determine whether the statement is true or false.
-$$\text { The function } f ( x ) = \frac { 1 } { x } \text { is decreasing on the interval } ( 0 , \infty )$$

Accepted Answer

A) True 
 B)False

Question 10

Solve the problem.
-The population of a city has varied considerably in recent years. The data in the table relates the population P to time t, in years, where t = 0 corresponds to 2006. Use a quadratic function fitted to
The data to predict the population in 2016.

Accepted Answer

A)  58,964 
B)  119,000 
C)  81,202 
D)  48,431 
A)  58,964 
B)  119,000 
C)  81,202 
D)  48,431

Question 11

Translate the given formula to an English phrase using the word ʺvariesʺ.
-$$\mathrm { A } = \frac { 1 } { 2 } \mathrm { bh } \text {, where } \mathrm { A } \text { is the area of a triangle with base } \mathrm { b } \text { and height }$$

Accepted Answer

The area of a triang

Question 12

Use the equation and the corresponding graph for the quadratic function to find what is requested.
-$f(x)=-2(x-2)^{2}+5$

Find the coordinates of the vertex.

Accepted Answer

A)  $( - 2,5 )$ 
B)  $( 5,2 )$ 
C)  $( 2,5 )$ 
D)  $( 2 , - 5 )$ 
A)  $( - 2,5 )$ 
B)  $( 5,2 )$ 
C)  $( 2,5 )$ 
D)  $( 2 , - 5 )$

Question 13

Solve the problem.
-$f(x)=(x+2)^{3}+5$

Accepted Answer

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

Question 14

Match the equation to the correct graph.
-$$y = 2 ( x - 3 ) ^ { 2 } - 2$$

Accepted Answer

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

Question 15

Find all rational zeros and factor f(x).
-$$f ( x ) = x ^ { 3 } - 6 x ^ { 2 } - x + 6$$

Accepted Answer

A)  $1 , - 1 , - 6 ; f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 6 )$ 
B)  $1 , - 2,8 ; f ( x ) = ( x - 1 ) ( x + 2 ) ( x -$ 
C)  $1 , - 1 , - 7 ; f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 7 )$ 
D)  $1 , - 1,6 ; f ( x ) = ( x - 1 ) ( x + 1 ) ( x -$ 
A)  $1 , - 1 , - 6 ; f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 6 )$ 
B)  $1 , - 2,8 ; f ( x ) = ( x - 1 ) ( x + 2 ) ( x -$ 
C)  $1 , - 1 , - 7 ; f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 7 )$ 
D)  $1 , - 1,6 ; f ( x ) = ( x - 1 ) ( x + 1 ) ( x -$

Question 16

Find the correct end behavior diagram for the given polynomial function.
-$$P ( x ) = - 3 x ^ { 3 } + 4 x ^ { 2 } + 2 x - 2$$

Accepted Answer

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

Question 17

Solve the problem.
-The student population of a small school has been increasing as shown in the following table.

Take 1910 as year zero, and determine the linear or quadratic function that best fits the data.

Accepted Answer

A)  $f ( x ) = 5 x - 93.2$ 
B)  $f ( x ) = 0.16 x ^ { 2 } - 17.5 x + 106$ 
C)  $f ( x ) = 0.1 x ^ { 2 } - 10 x + 440$ 
D)  $f ( x ) = 0.27 x ^ { 2 } - 29.1 x - 410$ 
A)  $f ( x ) = 5 x - 93.2$ 
B)  $f ( x ) = 0.16 x ^ { 2 } - 17.5 x + 106$ 
C)  $f ( x ) = 0.1 x ^ { 2 } - 10 x + 440$ 
D)  $f ( x ) = 0.27 x ^ { 2 } - 29.1 x - 410$

Question 18

Find a polynomial function f(x) of least possible degree having the graph shown.
-

Accepted Answer

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

Question 19

Use a graphing calculator to find the coordinates of the turning points of the graph of the polynomial function in the
indicated domain interval. Give answers to the nearest hundredth.
-$$f ( x ) = - x ^ { 3 } - 6 x ^ { 2 } + 37 x + 90 ; [ 2,3 ]$$

Accepted Answer

A)  $( - 6.04 , - 573.04 )$ 
B)  $( 2.04,132.02 )$ 
C)  $( 0 , - 10 )$ 
D)  $( - 3.50 , - 155.87 )$ 
A)  $( - 6.04 , - 573.04 )$ 
B)  $( 2.04,132.02 )$ 
C)  $( 0 , - 10 )$ 
D)  $( - 3.50 , - 155.87 )$

Question 20

Find the equation of the axis of symmetry of the parabola.
-$$f ( x ) = x ^ { 2 } - 4$$

Accepted Answer

A)  $y = 4$ 
B)  $x = - 4$ 
C)  $y = - 4$ 
D)  $x = 0$ 
A)  $y = 4$ 
B)  $x = - 4$ 
C)  $y = - 4$ 
D)  $x = 0$

Use the remainder theorem and synthetic division to find f(k). - $k = - 3 ; f ( x ) = 3 x ^ { 4 } + 5 x ^ { 3 } + 6 x ^ { 2 } - 6 x + 24$

Find all rational zeros and factor f(x). - $f ( x ) = x ^ { 3 } + 6 x ^ { 2 } - x - 6$

Find a polynomial of least degree with only real coefficients and having the given zeros. - $3 + \sqrt { 2 } , 3 - \sqrt { 2 }$ , and 2

Solve the problem. -In the following formula, $\mathrm { f } ( \mathrm { x } )$ is the minimum number of hours of studying required to attain a test score of $x : \quad f ( x ) = \frac { 0.41 x } { 100.5 - x }$ . How many hours of study are needed to score 91 ?

Find the domain and range of the function. - $f ( x ) = 3 x ^ { 2 } - 42 x + 151$

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

Find all rational zeros and factor f(x). - $f ( x ) = 8 x ^ { 3 } + 2 x ^ { 2 } - 5 x + 1$

Find a polynomial of least degree with only real coefficients and having the given zeros. - $4 + 2 i$ and $4 - 2 i$

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { 1 } { x } \text { is decreasing on the interval } ( 0 , \infty )$

Solve the problem. -The population of a city has varied considerably in recent years. The data in the table relates the population P to time t, in years, where t = 0 corresponds to 2006. Use a quadratic function fitted to The data to predict the population in 2016.

Translate the given formula to an English phrase using the word ʺvariesʺ. - $\mathrm { A } = \frac { 1 } { 2 } \mathrm { bh } \text {, where } \mathrm { A } \text { is the area of a triangle with base } \mathrm { b } \text { and height }$

Solve the problem. - $f(x)=(x+2)^{3}+5$ $Solve the problem. - f(x)=(x+2)^{3}+5$

Match the equation to the correct graph. - $y = 2 ( x - 3 ) ^ { 2 } - 2$

Find all rational zeros and factor f(x). - $f ( x ) = x ^ { 3 } - 6 x ^ { 2 } - x + 6$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = - 3 x ^ { 3 } + 4 x ^ { 2 } + 2 x - 2$

Solve the problem. -The student population of a small school has been increasing as shown in the following table. Take 1910 as year zero, and determine the linear or quadratic function that best fits the data.

Find a polynomial function f(x) of least possible degree having the graph shown. -

Use a graphing calculator to find the coordinates of the turning points of the graph of the polynomial function in the indicated domain interval. Give answers to the nearest hundredth. - $f ( x ) = - x ^ { 3 } - 6 x ^ { 2 } + 37 x + 90 ; [ 2,3 ]$

Find the equation of the axis of symmetry of the parabola. - $f ( x ) = x ^ { 2 } - 4$

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

Review of Basic Concepts

Filters

Exam 3: Polynomial and Rational Functions

Use the remainder theorem and synthetic division to find f(k). - k=−3;f(x)=3x4+5x3+6x2−6x+24k = - 3 ; f ( x ) = 3 x ^ { 4 } + 5 x ^ { 3 } + 6 x ^ { 2 } - 6 x + 24k=−3;f(x)=3x4+5x3+6x2−6x+24

Find all rational zeros and factor f(x). - f(x)=x3+6x2−x−6f ( x ) = x ^ { 3 } + 6 x ^ { 2 } - x - 6f(x)=x3+6x2−x−6

Find a polynomial of least degree with only real coefficients and having the given zeros. - 3+2,3−23 + \sqrt { 2 } , 3 - \sqrt { 2 }3+2​,3−2​ , and 2

Find the domain and range of the function. - f(x)=3x2−42x+151f ( x ) = 3 x ^ { 2 } - 42 x + 151f(x)=3x2−42x+151

Use synthetic division to perform the division. - x3−1x−1\frac { x ^ { 3 } - 1 } { x - 1 }x−1x3−1​

Find all rational zeros and factor f(x). - f(x)=8x3+2x2−5x+1f ( x ) = 8 x ^ { 3 } + 2 x ^ { 2 } - 5 x + 1f(x)=8x3+2x2−5x+1

Find a polynomial of least degree with only real coefficients and having the given zeros. - 4+2i4 + 2 i4+2i and 4−2i4 - 2 i4−2i

Determine whether the statement is true or false. - The function f(x)=1x is decreasing on the interval (0,∞)\text { The function } f ( x ) = \frac { 1 } { x } \text { is decreasing on the interval } ( 0 , \infty ) The function f(x)=x1​ is decreasing on the interval (0,∞)