Question 1

Find the correct end behavior diagram for the given polynomial function.
-$$P ( x ) = 6 x ^ { 6 } - x ^ { 5 } + 8 x ^ { 2 } - 3$$

Accepted Answer

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

Question 2

Graph the polynomial function. Factor first if the expression is not in factored form.
-$f(x)=-3 x^{2}(x+2)(x-1)$

Accepted Answer

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

Question 3

$$y \text { varies directly as } z \text { and } y = 306 \text { when } z = 18 \text {. Find } y \text { when } z \text { is } 19 \text {. }$$

Accepted Answer

A)  323 
B)  289 
C)  361 
D)  324 
A)  323 
B)  289 
C)  361 
D)  324

Question 4

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given.
-$f ( x ) = 9 x ^ { 4 } - 8 x ^ { 2 } - 7 ; 1$ and 2

Accepted Answer

A)  $f ( 1 ) = 6$ and $f ( 2 ) = - 105$ 
B)  $f ( 1 ) = - 5$ and $f ( 2 ) = 106$ 
C)  $f ( 1 ) = 6$ and $f ( 2 ) = 105$ 
D)  $f ( 1 ) = - 6$ and $f ( 2 ) = 105$ 
A)  $f ( 1 ) = 6$ and $f ( 2 ) = - 105$ 
B)  $f ( 1 ) = - 5$ and $f ( 2 ) = 106$ 
C)  $f ( 1 ) = 6$ and $f ( 2 ) = 105$ 
D)  $f ( 1 ) = - 6$ and $f ( 2 ) = 105$

Question 5

Find the domain and range of the function.
$f ( x ) = - 2 x ^ { 2 } - 36 x - 167$

Accepted Answer

A)  $\text { Domain: } ( - \infty , \infty ) \text {; Range: } ( - \infty , 9 ]$ 
B)  $\text { Domain: } ( - \infty , - 5 ] \text {; Range: } [ 0 , \infty )$ 
C)  $\text { Domain: } ( - \infty , - 5 ] \text {; Range: } [ 9 , \infty )$ 
D)  $\text { Domain: } ( - \infty , \infty ) \text {; Range: } ( - \infty , - 5 ]$ 
A)  $\text { Domain: } ( - \infty , \infty ) \text {; Range: } ( - \infty , 9 ]$ 
B)  $\text { Domain: } ( - \infty , - 5 ] \text {; Range: } [ 0 , \infty )$ 
C)  $\text { Domain: } ( - \infty , - 5 ] \text {; Range: } [ 9 , \infty )$ 
D)  $\text { Domain: } ( - \infty , \infty ) \text {; Range: } ( - \infty , - 5 ]$

Question 6

Use synthetic division to decide whether the given number k is a zero of the given polynomial function.
-$k = 2 + i ; f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 8 x + 10$

Accepted Answer

A) True 
 B)False

Question 7

Use the equation and the corresponding graph for the quadratic function to find what is requested.
-$f(x)=(x-1)^{2}-2$

Find the equation of the axis.

Accepted Answer

A)  $y = - 2$ 
B)  $y = 2$ 
C)  $x = - 1$ 
D)  $x = 1$ 
A)  $y = - 2$ 
B)  $y = 2$ 
C)  $x = - 1$ 
D)  $x = 1$

Question 8

Use synthetic division to perform the division.
-$$\frac { x ^ { 5 } - 3 x ^ { 4 } - 7 x ^ { 3 } - 13 x ^ { 2 } - 12 x + 13 } { x - 5 }$$

Accepted Answer

A)  $x ^ { 4 } + 2 x ^ { 3 } + 3 x ^ { 2 } + 2 x + 3$ 
B)  $x ^ { 3 } + 2 x ^ { 2 } + 3 x + 2 + \frac { 3 } { x - 5 }$ 
C)  $x ^ { 4 } + 2 x ^ { 3 } + 3 x ^ { 2 } + 2 x + 2 + \frac { 5 } { x - 5 }$ 
D)  $x ^ { 4 } + 2 x ^ { 3 } + 3 x ^ { 2 } + 2 x - 2 + \frac { 3 } { x - 5 }$ 
A)  $x ^ { 4 } + 2 x ^ { 3 } + 3 x ^ { 2 } + 2 x + 3$ 
B)  $x ^ { 3 } + 2 x ^ { 2 } + 3 x + 2 + \frac { 3 } { x - 5 }$ 
C)  $x ^ { 4 } + 2 x ^ { 3 } + 3 x ^ { 2 } + 2 x + 2 + \frac { 5 } { x - 5 }$ 
D)  $x ^ { 4 } + 2 x ^ { 3 } + 3 x ^ { 2 } + 2 x - 2 + \frac { 3 } { x - 5 }$

Question 9

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth.
-$$f ( x ) = x ^ { 3 } + x ^ { 2 } - 11 x - 11$$

Accepted Answer

A)  $1,3.3 , - 3.3$ 
B)  $1,5.5 , - 5.5$ 
C)  $1,3.3 \mathrm { i } , - 3.3 \mathrm { i }$ 
D)  $- 1,3.3 , - 3.3$ 
A)  $1,3.3 , - 3.3$ 
B)  $1,5.5 , - 5.5$ 
C)  $1,3.3 \mathrm { i } , - 3.3 \mathrm { i }$ 
D)  $- 1,3.3 , - 3.3$

Question 10

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the leading coefficient a of $x ^ { 2 }$ should be positive or negative.
-The amount of water in a pool as it is being filled, as a function of time.

Accepted Answer

A)  quadratic; negative 
B)  quadratic; positive 
C)  linear; positive 
D)  linear; negative 
A)  quadratic; negative 
B)  quadratic; positive 
C)  linear; positive 
D)  linear; negative

Question 11

The domain of a polynomial function is the set of all real numbers. What is the range of a polynomial function
of odd degree? One of even degree?

Accepted Answer

The answer of The domain of a polynomial function is...

Question 12

Give the equations of any vertical asymptotes.
-$$g ( x ) = \frac { x - 6 } { ( x - 4 ) ( x + 5 ) }$$

Accepted Answer

A)  $x = 4 , x = - 5$ 
B)  $x = 6$ 
C)  $x = - 6$ 
D)  $x = - 4 , x = 5$ 
A)  $x = 4 , x = - 5$ 
B)  $x = 6$ 
C)  $x = - 6$ 
D)  $x = - 4 , x = 5$

Question 13

Sketch the graph of the rational function.
-$$f ( x ) = \frac { x ^ { 2 } - 4 } { x - 2 }$$

Accepted Answer

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

Question 14

The concentration of a certain gas molecule in the atmosphere serves as an indicator of industrial air pollution. The data in the following table show the relationship of the estimated concentration of the molecule in the
Atmosphere, in parts per billion (ppb), to the year.

Determine the linear, quadratic, cubic, or quartic function that best fits the data.

Accepted Answer

A)  $f ( x ) = 0.00002 x ^ { 3 } - 0.003 x ^ { 2 } + 0.13 x + 2.4$ 
B)  $f ( x ) = 0.02 x + 2.90$ 
C)  $f ( x ) = x ^ { 4 } + 0.00002 x ^ { 3 } - 0.003 x ^ { 2 } + 0.13 x + 2.4$ 
D)  $f ( x ) = - 0.002 x ^ { 2 } + 0.11 x + 2.43$ 
A)  $f ( x ) = 0.00002 x ^ { 3 } - 0.003 x ^ { 2 } + 0.13 x + 2.4$ 
B)  $f ( x ) = 0.02 x + 2.90$ 
C)  $f ( x ) = x ^ { 4 } + 0.00002 x ^ { 3 } - 0.003 x ^ { 2 } + 0.13 x + 2.4$ 
D)  $f ( x ) = - 0.002 x ^ { 2 } + 0.11 x + 2.43$

Question 15

A furniture manufacturer decides to make a new line of desks. The table shows the profit, in thousands of dollars, for various levels of production. $$\begin{array} { c | c c c c c } 
\text { Number of } & & & & & \
\text { Desks Produced } & 120 & 350 & 500 & 650 & 750 \
\hline \text { Profit (Thousands) } & 13 & 37 & 44 & 34 & 25
\end{array}$$ Find a quadratic function to model the data, and use the model to predict the profit if 450 chairs are made. Round to the
Nearest thousand.

Accepted Answer

A)  $40,000 
B)  $44,000 
C)  $42,000 
D)  $45,000 
A)  $40,000 
B)  $44,000 
C)  $42,000 
D)  $45,000

Question 16

Use the factor theorem to decide whether or not the second polynomial is a factor of the first.
-$4 x ^ { 3 } + 10 x ^ { 2 } - 7 x + 3 ; x + 3$

Accepted Answer

A) True 
 B)False

Question 17

Use the graph to answer the question.
-Find the domain and range of the rational function graphed below.

Accepted Answer

A)  Domain: $( - \infty , - 3 ) \cup ( - 3 , \infty ) ;$ Range: $( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
B)  Domain: $( - \infty , - 2 ) \cup ( - 2 , \infty )$; Range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , - 2 ) \cup ( - 2 , \infty )$; Range: $( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
D)  Domain: $( - \infty , \infty )$; Range: $( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
A)  Domain: $( - \infty , - 3 ) \cup ( - 3 , \infty ) ;$ Range: $( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
B)  Domain: $( - \infty , - 2 ) \cup ( - 2 , \infty )$; Range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , - 2 ) \cup ( - 2 , \infty )$; Range: $( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
D)  Domain: $( - \infty , \infty )$; Range: $( - \infty , - 3 ) \cup ( - 3 , \infty )$

Question 18

Give the equation of any oblique asymptotes.
-$$f ( x ) = \frac { x ^ { 2 } - 2 x + 7 } { x + 5 }$$

Accepted Answer

A)  $x = y + 2$ 
B)  $y = x - 7$ 
C)  none 
D)  $y = x + 9$ 
A)  $x = y + 2$ 
B)  $y = x - 7$ 
C)  none 
D)  $y = x + 9$

Question 19

Given the equation or other information for a parabola, find the matching description or graph.
-$$\begin{array} { l } 
f ( x ) = a x ^ { 2 } + b x + c \
a > 0 ; b ^ { 2 } - 4 a c < 0
\end{array}$$

Accepted Answer

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

Question 20

Sketch the graph of the parabola.
-$$y = - \frac { 3 } { 2 } ( x + 4 ) ^ { 2 } - 3$$

Accepted Answer

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

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 6 x ^ { 6 } - x ^ { 5 } + 8 x ^ { 2 } - 3$

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=-3 x^{2}(x+2)(x-1)$ $Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=-3 x^{2}(x+2)(x-1)$

$y \text { varies directly as } z \text { and } y = 306 \text { when } z = 18 \text {. Find } y \text { when } z \text { is } 19 \text {. }$

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = 9 x ^ { 4 } - 8 x ^ { 2 } - 7 ; 1$ and 2

Find the domain and range of the function. $f ( x ) = - 2 x ^ { 2 } - 36 x - 167$

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = 2 + i ; f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 8 x + 10$

Use synthetic division to perform the division. - $\frac { x ^ { 5 } - 3 x ^ { 4 } - 7 x ^ { 3 } - 13 x ^ { 2 } - 12 x + 13 } { x - 5 }$

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - $f ( x ) = x ^ { 3 } + x ^ { 2 } - 11 x - 11$

The domain of a polynomial function is the set of all real numbers. What is the range of a polynomial function of odd degree? One of even degree?

Give the equations of any vertical asymptotes. - $g ( x ) = \frac { x - 6 } { ( x - 4 ) ( x + 5 ) }$

Sketch the graph of the rational function. - $f ( x ) = \frac { x ^ { 2 } - 4 } { x - 2 }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x ^ { 2 } - 4 } { x - 2 }$

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $4 x ^ { 3 } + 10 x ^ { 2 } - 7 x + 3 ; x + 3$

Use the graph to answer the question. -Find the domain and range of the rational function graphed below.

Give the equation of any oblique asymptotes. - $f ( x ) = \frac { x ^ { 2 } - 2 x + 7 } { x + 5 }$

Given the equation or other information for a parabola, find the matching description or graph. - f(x)=a+bx+c a>0;-4ac<0

Sketch the graph of the parabola. - $y = - \frac { 3 } { 2 } ( x + 4 ) ^ { 2 } - 3$ $Sketch the graph of the parabola. - y = - \frac { 3 } { 2 } ( x + 4 ) ^ { 2 } - 3$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 4: Polynomials and Rational Functions

Find the correct end behavior diagram for the given polynomial function. - P(x)=6x6−x5+8x2−3P ( x ) = 6 x ^ { 6 } - x ^ { 5 } + 8 x ^ { 2 } - 3P(x)=6x6−x5+8x2−3

Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=−3x2(x+2)(x−1)f(x)=-3 x^{2}(x+2)(x-1)f(x)=−3x2(x+2)(x−1)

y varies directly as z and y=306 when z=18. Find y when z is 19. y \text { varies directly as } z \text { and } y = 306 \text { when } z = 18 \text {. Find } y \text { when } z \text { is } 19 \text {. }y varies directly as z and y=306 when z=18. Find y when z is 19.

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - f(x)=9x4−8x2−7;1f ( x ) = 9 x ^ { 4 } - 8 x ^ { 2 } - 7 ; 1f(x)=9x4−8x2−7;1 and 2

Find the domain and range of the function. f(x)=−2x2−36x−167f ( x ) = - 2 x ^ { 2 } - 36 x - 167f(x)=−2x2−36x−167

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - k=2+i;f(x)=x3+3x2−8x+10k = 2 + i ; f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 8 x + 10k=2+i;f(x)=x3+3x2−8x+10

Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=(x−1)2−2f(x)=(x-1)^{2}-2f(x)=(x−1)2−2 Find the equation of the axis.

Use synthetic division to perform the division. - x5−3x4−7x3−13x2−12x+13x−5\frac { x ^ { 5 } - 3 x ^ { 4 } - 7 x ^ { 3 } - 13 x ^ { 2 } - 12 x + 13 } { x - 5 }x−5x5−3x4−7x3−13x2−12x+13​

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - f(x)=x3+x2−11x−11f ( x ) = x ^ { 3 } + x ^ { 2 } - 11 x - 11f(x)=x3+x2−11x−11

The domain of a polynomial function is the set of all real numbers. What is the range of a polynomial function of odd degree? One of even degree?

Give the equations of any vertical asymptotes. - g(x)=x−6(x−4)(x+5)g ( x ) = \frac { x - 6 } { ( x - 4 ) ( x + 5 ) }g(x)=(x−4)(x+5)x−6​

Sketch the graph of the rational function. - f(x)=x2−4x−2f ( x ) = \frac { x ^ { 2 } - 4 } { x - 2 }f(x)=x−2x2−4​

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - 4x3+10x2−7x+3;x+34 x ^ { 3 } + 10 x ^ { 2 } - 7 x + 3 ; x + 34x3+10x2−7x+3;x+3

Use the graph to answer the question. -Find the domain and range of the rational function graphed below.

Give the equation of any oblique asymptotes. - f(x)=x2−2x+7x+5f ( x ) = \frac { x ^ { 2 } - 2 x + 7 } { x + 5 }f(x)=x+5x2−2x+7​

Given the equation or other information for a parabola, find the matching description or graph. - f(x)=a+bx+c a>0;-4ac<0

Sketch the graph of the parabola. - y=−32(x+4)2−3y = - \frac { 3 } { 2 } ( x + 4 ) ^ { 2 } - 3y=−23​(x+4)2−3

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 6 x ^ { 6 } - x ^ { 5 } + 8 x ^ { 2 } - 3$

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=-3 x^{2}(x+2)(x-1)$ $Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=-3 x^{2}(x+2)(x-1)$

$y \text { varies directly as } z \text { and } y = 306 \text { when } z = 18 \text {. Find } y \text { when } z \text { is } 19 \text {. }$

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = 9 x ^ { 4 } - 8 x ^ { 2 } - 7 ; 1$ and 2

Find the domain and range of the function. $f ( x ) = - 2 x ^ { 2 } - 36 x - 167$

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = 2 + i ; f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 8 x + 10$

Use synthetic division to perform the division. - $\frac { x ^ { 5 } - 3 x ^ { 4 } - 7 x ^ { 3 } - 13 x ^ { 2 } - 12 x + 13 } { x - 5 }$

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - $f ( x ) = x ^ { 3 } + x ^ { 2 } - 11 x - 11$

Give the equations of any vertical asymptotes. - $g ( x ) = \frac { x - 6 } { ( x - 4 ) ( x + 5 ) }$

Sketch the graph of the rational function. - $f ( x ) = \frac { x ^ { 2 } - 4 } { x - 2 }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x ^ { 2 } - 4 } { x - 2 }$

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $4 x ^ { 3 } + 10 x ^ { 2 } - 7 x + 3 ; x + 3$

Give the equation of any oblique asymptotes. - $f ( x ) = \frac { x ^ { 2 } - 2 x + 7 } { x + 5 }$

Sketch the graph of the parabola. - $y = - \frac { 3 } { 2 } ( x + 4 ) ^ { 2 } - 3$ $Sketch the graph of the parabola. - y = - \frac { 3 } { 2 } ( x + 4 ) ^ { 2 } - 3$