Question 1

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

Accepted Answer

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

Question 2

Give the equations of any horizontal asymptotes.
-$$h ( x ) = \frac { 2 - 4 x } { - 6 x + 3 }$$

Accepted Answer

A)  $y = \frac { 2 } { 3 }$ 
B)  none 
C)  $y = 0$ 
D)  $y = - \frac { 2 } { 3 }$ 
A)  $y = \frac { 2 } { 3 }$ 
B)  none 
C)  $y = 0$ 
D)  $y = - \frac { 2 } { 3 }$

Question 3

Identify the vertex of the parabola.
-$$y = x ^ { 2 } - 12 x + 44$$

Accepted Answer

A)  $( 0,6 )$ 
B)  $( 8,6 )$ 
C)  $( 6,8 )$ 
D)  $( 8,0 )$ 
A)  $( 0,6 )$ 
B)  $( 8,6 )$ 
C)  $( 6,8 )$ 
D)  $( 8,0 )$

Question 4

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 5

Solve the problem
-Bob owns a watch repair shop. He has found that the cost of operating his shop is given by $c ( x ) = 4 x ^ { 2 } - 208 x + 49$, where $c$ is cost and $x$ is the number of watches repaired. How many watches must he repair to have the lowest cost?

Accepted Answer

A)  26 watches 
B)  49 watches 
C)  40 watches 
D)  24 watches 
A)  26 watches 
B)  49 watches 
C)  40 watches 
D)  24 watches

Question 6

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

Accepted Answer

A)  $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } + 21 x + 20$ 
B)  $f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 20 x + 20$ 
C)  $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + 21 x - 20$ 
D)  $f ( x ) = x ^ { 3 } - 4 x ^ { 2 } - ( 3 - 4 i ) x + 12 + 16 i$ 
A)  $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } + 21 x + 20$ 
B)  $f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 20 x + 20$ 
C)  $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + 21 x - 20$ 
D)  $f ( x ) = x ^ { 3 } - 4 x ^ { 2 } - ( 3 - 4 i ) x + 12 + 16 i$

Question 7

Find an equation for the rational function graph.
-If the average cost per unit $C ( x )$ to produce $x$ units of plywood is given by $C ( x ) = \frac { 1500 } { x + 50 }$, what do 1000 units cost?

Accepted Answer

A)  $\$ 30,000.00$ 
B)  $\$ 1428.57$ 
C)  $\$ 1499.95$ 
D)  $\$ 500.00$ 
A)  $\$ 30,000.00$ 
B)  $\$ 1428.57$ 
C)  $\$ 1499.95$ 
D)  $\$ 500.00$

Question 8

Solve the problem
-The length of a table is 17 inches more than its width. If the area of the table is 2280 square inches, what is its length?

Accepted Answer

A)  $80 \mathrm { in }$. 
B)  $23 \mathrm { in }$. 
C)  $40 \mathrm { in }$. 
D)  $57 \mathrm { in }$. 
A)  $80 \mathrm { in }$. 
B)  $23 \mathrm { in }$. 
C)  $40 \mathrm { in }$. 
D)  $57 \mathrm { in }$.

Question 9

Find a polynomial of least degree with only real coefficients and having the given zeros.
-$1 - \sqrt { 3 } , 1 + \sqrt { 3 }$, and $1 + i$

Accepted Answer

A)  $f ( x ) = x ^ { 4 } + 3 x ^ { 3 } + 4 x ^ { 2 } - 1$ 
B)  $f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 8 x ^ { 2 } - 4$ 
C)  $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + 4 x ^ { 2 } - 4$ 
D)  $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 4 x ^ { 2 } - 4$ 
A)  $f ( x ) = x ^ { 4 } + 3 x ^ { 3 } + 4 x ^ { 2 } - 1$ 
B)  $f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 8 x ^ { 2 } - 4$ 
C)  $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + 4 x ^ { 2 } - 4$ 
D)  $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 4 x ^ { 2 } - 4$

Question 10

Find the domain and range of the function.
-$$f ( x ) = 10 x ^ { 2 } - 60 x + 100$$

Accepted Answer

A)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 0 ]$ 
B)  Domain: $( - \infty , \infty )$; Range: $[ 0 , \infty )$ 
C)  Domain: $( - \infty , \infty )$; Range: $[ 10 , \infty )$ 
D)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 3 ]$ 
A)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 0 ]$ 
B)  Domain: $( - \infty , \infty )$; Range: $[ 0 , \infty )$ 
C)  Domain: $( - \infty , \infty )$; Range: $[ 10 , \infty )$ 
D)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 3 ]$

Question 11

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

Accepted Answer

A)  Domain: $( - \infty , - 1 ) \cup ( - 1 , \infty )$; Range: $( - \infty , 2 ) \cup ( 2 , \infty )$ 
B)  Domain: $( - \infty , - 1 ) \cup ( - 1 , \infty )$; Range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 2 ) \cup ( 2 , \infty )$ 
D)  Domain: $( - \infty , 2 ) \cup ( 2 , \infty )$; Range: $( - \infty , - 1 ) \cup ( - 1 , \infty )$ 
A)  Domain: $( - \infty , - 1 ) \cup ( - 1 , \infty )$; Range: $( - \infty , 2 ) \cup ( 2 , \infty )$ 
B)  Domain: $( - \infty , - 1 ) \cup ( - 1 , \infty )$; Range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 2 ) \cup ( 2 , \infty )$ 
D)  Domain: $( - \infty , 2 ) \cup ( 2 , \infty )$; Range: $( - \infty , - 1 ) \cup ( - 1 , \infty )$

Question 12

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

Accepted Answer

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

Question 13

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 height of a ball thrown from the ground, as a function of time.

Accepted Answer

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

Question 14

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.
-$$f ( x ) = - 2 x ^ { 3 } - 10 x ^ { 2 } + 82 x + 90 ; [ 2,3 ]$$

Accepted Answer

A)  $( 2.39,201.56 )$ 
B)  $( - 5.72 , - 893.92 )$ 
C)  $( 0,45 )$ 
D)  $( - 5.50 , - 829.87 )$ 
A)  $( 2.39,201.56 )$ 
B)  $( - 5.72 , - 893.92 )$ 
C)  $( 0,45 )$ 
D)  $( - 5.50 , - 829.87 )$

Question 15

Find the equation of the axis of symmetry of the parabola.
-$$y = x ^ { 2 } - 20 x + 109$$

Accepted Answer

A)  $x = - 10$ 
B)  $x = 10$ 
C)  $x = 0$ 
D)  $x = 9$ 
A)  $x = - 10$ 
B)  $x = 10$ 
C)  $x = 0$ 
D)  $x = 9$

Question 16

Use the factor theorem to decide whether or not the second polynomial is a factor of the first.
-$5 x ^ { 3 } + 8 x ^ { 2 } - 3 x + 2 ; x + 2$

Accepted Answer

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

Question 17

Round your answer to two decimal places.
-If $\mathrm { f }$ varies jointly as $\mathrm { q } ^ { 2 }$ and $\mathrm { h }$, and $\mathrm { f } = 81$ when $\mathrm { q } = 3$ and $\mathrm { h } = 3$, find $\mathrm { f }$ when $\mathrm { q } = 4$ and $\mathrm { h } = 2$.

Accepted Answer

A)  24 
B)  48 
C)  6 
D)  96 
A)  24 
B)  48 
C)  6 
D)  96

Question 18

Use the equation and the corresponding graph for the quadratic function to find what is requested.
-$$f ( x ) = - 2 ( x - 5 ) ^ { 2 } + 3$$
 
 Find the equation of the axis.

Accepted Answer

A)  x = 5 
B)  x = 3 
C)  y = 3 
D)  y = 5 
A)  x = 5 
B)  x = 3 
C)  y = 3 
D)  y = 5

Question 19

Use the equation and the corresponding graph for the quadratic function to find what is requested.
-$f(x)=-2(x-2)^{2}+3$
 
 Find the $y$-intercept.

Accepted Answer

A)  $( 0 , - 4 )$ 
B)  $( - 5,0 )$ 
C)  $( 0 , - 6 )$ 
D)  $( 0 , - 5 )$ 
A)  $( 0 , - 4 )$ 
B)  $( - 5,0 )$ 
C)  $( 0 , - 6 )$ 
D)  $( 0 , - 5 )$

Question 20

Use synthetic division to perform the division.
-$$\frac { - 6 x ^ { 3 } + 2 x ^ { 2 } + 5 x - 10 } { x - 2 }$$

Accepted Answer

A)  $- 6 x ^ { 2 } - 10 x - 15 + \frac { - 25 } { x - 2 }$ 
B)  $- 6 x ^ { 2 } - 10 x - 15 + \frac { - 40 } { x - 2 }$ 
C)  $- 6 x ^ { 2 } - 10 x - 25 + \frac { - 40 } { x - 2 }$ 
D)  $- 6 x ^ { 2 } - 10 x - 5 + \frac { - 10 } { x - 2 }$ 
A)  $- 6 x ^ { 2 } - 10 x - 15 + \frac { - 25 } { x - 2 }$ 
B)  $- 6 x ^ { 2 } - 10 x - 15 + \frac { - 40 } { x - 2 }$ 
C)  $- 6 x ^ { 2 } - 10 x - 25 + \frac { - 40 } { x - 2 }$ 
D)  $- 6 x ^ { 2 } - 10 x - 5 + \frac { - 10 } { x - 2 }$

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

Give the equations of any horizontal asymptotes. - $h ( x ) = \frac { 2 - 4 x } { - 6 x + 3 }$

Identify the vertex of the parabola. - $y = x ^ { 2 } - 12 x + 44$

Solve the problem -Bob owns a watch repair shop. He has found that the cost of operating his shop is given by $c ( x ) = 4 x ^ { 2 } - 208 x + 49$ , where $c$ is cost and $x$ is the number of watches repaired. How many watches must he repair to have the lowest cost?

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

Find an equation for the rational function graph. -If the average cost per unit $C ( x )$ to produce $x$ units of plywood is given by $C ( x ) = \frac { 1500 } { x + 50 }$ , what do 1000 units cost?

Solve the problem -The length of a table is 17 inches more than its width. If the area of the table is 2280 square inches, what is its length?

Find a polynomial of least degree with only real coefficients and having the given zeros. - $1 - \sqrt { 3 } , 1 + \sqrt { 3 }$ , and $1 + i$

Find the domain and range of the function. - $f ( x ) = 10 x ^ { 2 } - 60 x + 100$

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

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

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. - $f ( x ) = - 2 x ^ { 3 } - 10 x ^ { 2 } + 82 x + 90 ; [ 2,3 ]$

Find the equation of the axis of symmetry of the parabola. - $y = x ^ { 2 } - 20 x + 109$

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $5 x ^ { 3 } + 8 x ^ { 2 } - 3 x + 2 ; x + 2$

Round your answer to two decimal places. -If $\mathrm { f }$ varies jointly as $\mathrm { q } ^ { 2 }$ and $\mathrm { h }$ , and $\mathrm { f } = 81$ when $\mathrm { q } = 3$ and $\mathrm { h } = 3$ , find $\mathrm { f }$ when $\mathrm { q } = 4$ and $\mathrm { h } = 2$ .

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=-2(x-2)^{2}+3$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=-2(x-2)^{2}+3 Find the y -intercept.$ Find the $y$ -intercept.

Use synthetic division to perform the division. - $\frac { - 6 x ^ { 3 } + 2 x ^ { 2 } + 5 x - 10 } { x - 2 }$

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

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

Give the equations of any horizontal asymptotes. - h(x)=2−4x−6x+3h ( x ) = \frac { 2 - 4 x } { - 6 x + 3 }h(x)=−6x+32−4x​

Identify the vertex of the parabola. - y=x2−12x+44y = x ^ { 2 } - 12 x + 44y=x2−12x+44

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

Find a polynomial of least degree with only real coefficients and having the given zeros. - 2+i,42 + i , 42+i,4

Find an equation for the rational function graph. -If the average cost per unit C(x)C ( x )C(x) to produce xxx units of plywood is given by C(x)=1500x+50C ( x ) = \frac { 1500 } { x + 50 }C(x)=x+501500​ , what do 1000 units cost?