Question 1

Using a graphing utility, graph $f ( x ) = x ^ { 5 } - 14 x ^ { 4 } + 49 x ^ { 3 }$ and approximate the zeros and their multiplicity.

Accepted Answer

A)  $x = 0 , \text { multiplicity } 2 ; x = 7 , \text { multiplicity } 3$ 
B)  $x = 0 , \text { multiplicity } 1 ; x = 7 , \text { multiplicity } 1 ; x = - 7 , \text { multiplicity } 1 ; x = \text { \#\# } \mathrm { b } = \mathrm { m } , \text { multiplicity } 1$ 
C)  $x = 0 , \text { multiplicity } 3 ; x = 7 , \text { multiplicity } 2$ 
D)  $x = 0 , \text { multiplicity } 3 ; x = - 7 , \text { multiplicity } 2$ 
E)  $x = 0 \text {, multiplicity } 2 ; x = 7 \text {, multiplicity } 2 ; x = - 7 \text {, multiplicity } 1$ 
A)  $x = 0 , \text { multiplicity } 2 ; x = 7 , \text { multiplicity } 3$ 
B)  $x = 0 , \text { multiplicity } 1 ; x = 7 , \text { multiplicity } 1 ; x = - 7 , \text { multiplicity } 1 ; x = \text { \#\# } \mathrm { b } = \mathrm { m } , \text { multiplicity } 1$ 
C)  $x = 0 , \text { multiplicity } 3 ; x = 7 , \text { multiplicity } 2$ 
D)  $x = 0 , \text { multiplicity } 3 ; x = - 7 , \text { multiplicity } 2$ 
E)  $x = 0 \text {, multiplicity } 2 ; x = 7 \text {, multiplicity } 2 ; x = - 7 \text {, multiplicity } 1$

Question 2

Do the operation and express the answer in a + bi form. 
 $( 5 - \sqrt { - 25 } ) - ( 2 i - 3 )$

Accepted Answer

A) - 8 + 14i 
B) 8 + 7i 
C) - 8 + 7i 
D) - 8 - 7i 
E) 8 - 7i 
A) - 8 + 14i 
B) 8 + 7i 
C) - 8 + 7i 
D) - 8 - 7i 
E) 8 - 7i

Question 3

Determine the value that the function f approaches as the magnitude of x increases.   $f ( x ) = \frac { 3 x - 1 } { x - 4 }$

Accepted Answer

A) $\infty$ 
B)  -4 
C)  3 
D) -1 
E) 0 
A) $\infty$ 
B)  -4 
C)  3 
D) -1 
E) 0

Question 4

The cost C (in millions of dollars) of removing p% of the industrial and municipal pollutants discharged into a river is given by
  $C = \frac { 235 p } { 100 - p } , 0 \leq p < 100$ .
 
According to this model, would it be possible to remove 100% of the pollutants? Explain.

Accepted Answer

A) True 
 B)False

Question 5

Select from the following which is the polynomial function that has the given zeros.   $0 , - 7 , - 3$

Accepted Answer

A)  $f ( x ) = - x ^ { 3 } + 10 x ^ { 2 } + 21 x$ 
B)  $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 21 x$ 
C)  $f ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 21 x$ 
D)  $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } - 21 x$ 
E)  $f ( x ) = x ^ { 3 } + 10 x ^ { 2 } - 21 x$ 
A)  $f ( x ) = - x ^ { 3 } + 10 x ^ { 2 } + 21 x$ 
B)  $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 21 x$ 
C)  $f ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 21 x$ 
D)  $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } - 21 x$ 
E)  $f ( x ) = x ^ { 3 } + 10 x ^ { 2 } - 21 x$

Question 6

The total revenue R earned per day (in dollars) from a pet-sitting service is given by   $R ( p ) = - 12 p ^ { 2 } + 150 p$  
Where p is the price charged per pet (in dollars).
 
Find the revenue when the price per pet is $3.

Accepted Answer

A) $372.00 
B) $352.00 
C) $382.00 
D) $362.00 
E) $342.00 
A) $372.00 
B) $352.00 
C) $382.00 
D) $362.00 
E) $342.00

Question 7

A manufacturer of lighting fixtures has daily production costs of $C = 800 - 80 x + 0.25 x ^ { 2 }$ where C is the total cost (in dollars) and x is the number of units produced.How many fixtures should be produced each day to yield a minimum cost? (Round your answer to two decimal places.)

Accepted Answer

A) 160 
B) 106.67 
C) 320 
D) 400 
E) 800 
A) 160 
B) 106.67 
C) 320 
D) 400 
E) 800

Question 8

Find the vertex of the parabolic graph of the equation. y = 4(x - 5) 2 + 7

Accepted Answer

A) (5, 0) 
B) (25, 7) 
C) (5, 4) 
D) (7, 5) 
E) (5, 7) 
A) (5, 0) 
B) (25, 7) 
C) (5, 4) 
D) (7, 5) 
E) (5, 7)

Question 9

Select the graph of the function $y = [ 2 ( x - 1 ) ] ^ { 2 } + 1$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .

Accepted Answer

A)     Horizontal shift of 4 units to the right and vertical shift of 1 unit upward and horizontal shrink 
B)      Horizontal shift of 2 units to the right and vertical shift of 1 unit upward and horizontal shrink 
C)     Horizontal shift of 5 units to the right and vertical shift of 1 unit upward and horizontal shrink 
D)     Horizontal shift of 1 units to the right and vertical shift of 1 unit upward and horizontal shrink 
E)      Horizontal shift of 3 units to the right and vertical shift of 1 unit upward and horizontal shrink 
A)     Horizontal shift of 4 units to the right and vertical shift of 1 unit upward and horizontal shrink 
B)      Horizontal shift of 2 units to the right and vertical shift of 1 unit upward and horizontal shrink 
C)     Horizontal shift of 5 units to the right and vertical shift of 1 unit upward and horizontal shrink 
D)     Horizontal shift of 1 units to the right and vertical shift of 1 unit upward and horizontal shrink 
E)      Horizontal shift of 3 units to the right and vertical shift of 1 unit upward and horizontal shrink

Question 10

Write the function in the form f(x) = (x - k)q(x) + r for the given value of k and demonstrate that f(k) = r.  $f ( x ) = x ^ { 3 } - 1 x ^ { 2 } - 14 x + 12 \quad k = 4$

Accepted Answer

A)  $( x - 4 ) \left( x ^ { 2 } - 3 x - 2 \right) + 4$ 
B)  $( x + 4 ) \left( x ^ { 2 } + 3 x - 2 \right) + 4$ 
C)  $( x - 4 ) \left( x ^ { 2 } + 3 x - 2 \right) + 4$ 
D)  $( x - 4 ) \left( x ^ { 2 } + 3 x - 2 \right) - 4$ 
E)  $( x - 4 ) \left( x ^ { 2 } - 3 x - 2 \right) + 4$. 
A)  $( x - 4 ) \left( x ^ { 2 } - 3 x - 2 \right) + 4$ 
B)  $( x + 4 ) \left( x ^ { 2 } + 3 x - 2 \right) + 4$ 
C)  $( x - 4 ) \left( x ^ { 2 } + 3 x - 2 \right) + 4$ 
D)  $( x - 4 ) \left( x ^ { 2 } + 3 x - 2 \right) - 4$ 
E)  $( x - 4 ) \left( x ^ { 2 } - 3 x - 2 \right) + 4$.

Question 11

An open box is to be made from a square piece of cardboard, $66 \text { inches }$ on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).After determining the function V, in terms of x, that represents the volume of the box, use a graphing utility to estimate the dimensions that will maximize its volume.

Accepted Answer

A)  $22 ^ { \prime \prime } \times 22 ^ { \prime \prime } \times 11 ^ { \prime \prime }$ 
B)  $44 ^ { \prime \prime } \times 44 ^ { \prime \prime } \times 11 ^ { \prime \prime }$ 
C)  $44 ^ { \prime \prime } \times 44 ^ { \prime \prime } \times 22 ^ { \prime \prime }$ 
D)  $33 ^ { \prime \prime } \times 33 ^ { \prime \prime } \times 22 ^ { \prime \prime }$ 
E)  $11 ^ { \prime \prime } \times 11 ^ { \prime \prime } \times 5.5 ^ { \prime \prime }$ 
A)  $22 ^ { \prime \prime } \times 22 ^ { \prime \prime } \times 11 ^ { \prime \prime }$ 
B)  $44 ^ { \prime \prime } \times 44 ^ { \prime \prime } \times 11 ^ { \prime \prime }$ 
C)  $44 ^ { \prime \prime } \times 44 ^ { \prime \prime } \times 22 ^ { \prime \prime }$ 
D)  $33 ^ { \prime \prime } \times 33 ^ { \prime \prime } \times 22 ^ { \prime \prime }$ 
E)  $11 ^ { \prime \prime } \times 11 ^ { \prime \prime } \times 5.5 ^ { \prime \prime }$

Question 12

Find real numbers a and b such that the equation is true. 
 $a + b i = - 8 + 18 i$

Accepted Answer

A)  $a = - 12 , b = 22$ 
B)  $a = - 10 , b = 20$ 
C)   $a = - 11 , b = 21$ 
D)  $a = - 9 , b = 19$ 
E)  $a = - 8 , b = 18$ 
A)  $a = - 12 , b = 22$ 
B)  $a = - 10 , b = 20$ 
C)   $a = - 11 , b = 21$ 
D)  $a = - 9 , b = 19$ 
E)  $a = - 8 , b = 18$

Question 13

Find all the real zeros of the polynomial function.   $f ( x ) = x ^ { 2 } - 9$

Accepted Answer

A)  $- 9$ 
B)  $3$ 
C)  $- 3$ 
D)  $9$ 
E)  $\pm 3$ 
A)  $- 9$ 
B)  $3$ 
C)  $- 3$ 
D)  $9$ 
E)  $\pm 3$

Question 14

Select the graph of the function $y = ( x / 3 ) ^ { 2 } - 3$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .

Accepted Answer

A)     Horizontal stretch and vertical shift. 
B)     Horizontal stretch and vertical shift. 
C)     Horizontal stretch and vertical shift. 
D)     Horizontal stretch and vertical shift. 
E)      Horizontal stretch and vertical shift. 
A)     Horizontal stretch and vertical shift. 
B)     Horizontal stretch and vertical shift. 
C)     Horizontal stretch and vertical shift. 
D)     Horizontal stretch and vertical shift. 
E)      Horizontal stretch and vertical shift.

Question 15

Graph the polynomial function. 
 $y = - x ^ { 3 } + 3$

Accepted Answer

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

Question 16

Solve the inequality and graph the solution on the real number line.
 $9 x ^ { 2 } - 6 x + 1 \leq 0$

Accepted Answer

A)   $x = 3$   
B)  $x = \frac { 1 } { 3 }$   
C)  $x = \frac { 1 } { 9 }$   
D)  $x = - \frac { 1 } { 3 }$   
E)  $x = - 3$   
A)   $x = 3$   
B)  $x = \frac { 1 } { 3 }$   
C)  $x = \frac { 1 } { 9 }$   
D)  $x = - \frac { 1 } { 3 }$   
E)  $x = - 3$

Question 17

Let $P ( x ) = 2 x ^ { 3 } + 9 x ^ { 2 } - 7 x + 3$ .
​
Use synthetic division to find the value P (-7).

Accepted Answer

The answer of Let \(P ( x ) = 2...

Question 18

The graph of the function  
  $$f ( x ) = \frac { 3 x } { x ^ { 2 } - 4 }$$ is shown below.Determine the domain.

Accepted Answer

A) Domain: all real numbers except x = -2 and x = 2 
B) Domain: all real numbers except x = 2 
C) Domain: all real numbers except x = 0 
D) Domain: all real numbers except x = 1 
E) Domain: all real numbers except x = 4 
A) Domain: all real numbers except x = -2 and x = 2 
B) Domain: all real numbers except x = 2 
C) Domain: all real numbers except x = 0 
D) Domain: all real numbers except x = 1 
E) Domain: all real numbers except x = 4

Question 19

Find the domain of x in the expression.  
 $\sqrt { \frac { x } { x ^ { 2 } - 2 x - 24 } }$

Accepted Answer

A)  $( - 4,0 ] \cap ( 6 , \infty )$ 
B)  $( - 6,0 ] \cup ( 4 , \infty )$ 
C)  $( - 4,0 ] \cup ( 6 , \infty )$ 
D)  $( - 4,0 ] \cup ( - 6 , \infty )$ 
E)  $( - 6,0 ] \cap ( - 4 , \infty )$ 
A)  $( - 4,0 ] \cap ( 6 , \infty )$ 
B)  $( - 6,0 ] \cup ( 4 , \infty )$ 
C)  $( - 4,0 ] \cup ( 6 , \infty )$ 
D)  $( - 4,0 ] \cup ( - 6 , \infty )$ 
E)  $( - 6,0 ] \cap ( - 4 , \infty )$

Question 20

Select the graph of the function $y = \frac { 3 } { 2 } x ^ { 2 }$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .

Accepted Answer

A)    Vertical shrink. 
B)     Vertical stretch. 
C)      Vertical stretch and reflection in the x-axis. 
D)     Vertical shrink. 
E)     Vertical stretch and reflection in the x-axis. 
A)    Vertical shrink. 
B)     Vertical stretch. 
C)      Vertical stretch and reflection in the x-axis. 
D)     Vertical shrink. 
E)     Vertical stretch and reflection in the x-axis.

Using a graphing utility, graph $f ( x ) = x ^ { 5 } - 14 x ^ { 4 } + 49 x ^ { 3 }$ and approximate the zeros and their multiplicity.

Do the operation and express the answer in a + bi form. $( 5 - \sqrt { - 25 } ) - ( 2 i - 3 )$

Determine the value that the function f approaches as the magnitude of x increases. $f ( x ) = \frac { 3 x - 1 } { x - 4 }$

The cost C (in millions of dollars) of removing p% of the industrial and municipal pollutants discharged into a river is given by $C = \frac { 235 p } { 100 - p } , 0 \leq p < 100$ . According to this model, would it be possible to remove 100% of the pollutants? Explain.

Select from the following which is the polynomial function that has the given zeros. $0 , - 7 , - 3$

The total revenue R earned per day (in dollars) from a pet-sitting service is given by $R ( p ) = - 12 p ^ { 2 } + 150 p$ Where p is the price charged per pet (in dollars). Find the revenue when the price per pet is $3.

A manufacturer of lighting fixtures has daily production costs of $C = 800 - 80 x + 0.25 x ^ { 2 }$ where C is the total cost (in dollars) and x is the number of units produced.How many fixtures should be produced each day to yield a minimum cost? (Round your answer to two decimal places.)

Find the vertex of the parabolic graph of the equation. y = 4(x - 5) ² + 7

Select the graph of the function $y = [ 2 ( x - 1 ) ] ^ { 2 } + 1$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .

Write the function in the form f(x) = (x - k)q(x) + r for the given value of k and demonstrate that f(k) = r. $f ( x ) = x ^ { 3 } - 1 x ^ { 2 } - 14 x + 12 \quad k = 4$

Find real numbers a and b such that the equation is true. $a + b i = - 8 + 18 i$

Find all the real zeros of the polynomial function. $f ( x ) = x ^ { 2 } - 9$

Select the graph of the function $y = ( x / 3 ) ^ { 2 } - 3$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .

Graph the polynomial function. $y = - x ^ { 3 } + 3$

Solve the inequality and graph the solution on the real number line. $9 x ^ { 2 } - 6 x + 1 \leq 0$

Let $P ( x ) = 2 x ^ { 3 } + 9 x ^ { 2 } - 7 x + 3$ . Use synthetic division to find the value P (-7).

The graph of the function $f ( x ) = \frac { 3 x } { x ^ { 2 } - 4 }$ is shown below.Determine the domain. $The graph of the function f ( x ) = \frac { 3 x } { x ^ { 2 } - 4 } is shown below.Determine the domain.$

Find the domain of x in the expression. $\sqrt { \frac { x } { x ^ { 2 } - 2 x - 24 } }$

Select the graph of the function $y = \frac { 3 } { 2 } x ^ { 2 }$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 2: Polynomial and Rational Functions

Using a graphing utility, graph f(x)=x5−14x4+49x3f ( x ) = x ^ { 5 } - 14 x ^ { 4 } + 49 x ^ { 3 }f(x)=x5−14x4+49x3 and approximate the zeros and their multiplicity.

Do the operation and express the answer in a + bi form. (5−−25)−(2i−3)( 5 - \sqrt { - 25 } ) - ( 2 i - 3 )(5−−25​)−(2i−3)

Determine the value that the function f approaches as the magnitude of x increases. f(x)=3x−1x−4f ( x ) = \frac { 3 x - 1 } { x - 4 }f(x)=x−43x−1​

Select from the following which is the polynomial function that has the given zeros. 0,−7,−30 , - 7 , - 30,−7,−3

The total revenue R earned per day (in dollars) from a pet-sitting service is given by R(p)=−12p2+150pR ( p ) = - 12 p ^ { 2 } + 150 pR(p)=−12p2+150p Where p is the price charged per pet (in dollars). Find the revenue when the price per pet is $3.

Find the vertex of the parabolic graph of the equation. y = 4(x - 5) 2 + 7

Select the graph of the function y=[2(x−1)]2+1y = [ 2 ( x - 1 ) ] ^ { 2 } + 1y=[2(x−1)]2+1 .Compare the graph of this function with the graph of y=x2y = x ^ { 2 }y=x2 .

Write the function in the form f(x) = (x - k)q(x) + r for the given value of k and demonstrate that f(k) = r. f(x)=x3−1x2−14x+12k=4f ( x ) = x ^ { 3 } - 1 x ^ { 2 } - 14 x + 12 \quad k = 4f(x)=x3−1x2−14x+12k=4

Find real numbers a and b such that the equation is true. a+bi=−8+18ia + b i = - 8 + 18 ia+bi=−8+18i

Find all the real zeros of the polynomial function. f(x)=x2−9f ( x ) = x ^ { 2 } - 9f(x)=x2−9

Select the graph of the function y=(x/3)2−3y = ( x / 3 ) ^ { 2 } - 3y=(x/3)2−3 .Compare the graph of this function with the graph of y=x2y = x ^ { 2 }y=x2 .

Graph the polynomial function. y=−x3+3y = - x ^ { 3 } + 3y=−x3+3

Solve the inequality and graph the solution on the real number line. 9x2−6x+1≤09 x ^ { 2 } - 6 x + 1 \leq 09x2−6x+1≤0

Let P(x)=2x3+9x2−7x+3P ( x ) = 2 x ^ { 3 } + 9 x ^ { 2 } - 7 x + 3P(x)=2x3+9x2−7x+3 . ​ Use synthetic division to find the value P (-7).

The graph of the function f(x)=3xx2−4f ( x ) = \frac { 3 x } { x ^ { 2 } - 4 }f(x)=x2−43x​ is shown below.Determine the domain.

Find the domain of x in the expression. xx2−2x−24\sqrt { \frac { x } { x ^ { 2 } - 2 x - 24 } }x2−2x−24x​​

Select the graph of the function y=32x2y = \frac { 3 } { 2 } x ^ { 2 }y=23​x2 .Compare the graph of this function with the graph of y=x2y = x ^ { 2 }y=x2 .

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Using a graphing utility, graph $f ( x ) = x ^ { 5 } - 14 x ^ { 4 } + 49 x ^ { 3 }$ and approximate the zeros and their multiplicity.

Do the operation and express the answer in a + bi form. $( 5 - \sqrt { - 25 } ) - ( 2 i - 3 )$

Determine the value that the function f approaches as the magnitude of x increases. $f ( x ) = \frac { 3 x - 1 } { x - 4 }$

Select from the following which is the polynomial function that has the given zeros. $0 , - 7 , - 3$

The total revenue R earned per day (in dollars) from a pet-sitting service is given by $R ( p ) = - 12 p ^ { 2 } + 150 p$ Where p is the price charged per pet (in dollars). Find the revenue when the price per pet is $3.

Find the vertex of the parabolic graph of the equation. y = 4(x - 5) ² + 7

Select the graph of the function $y = [ 2 ( x - 1 ) ] ^ { 2 } + 1$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .

Write the function in the form f(x) = (x - k)q(x) + r for the given value of k and demonstrate that f(k) = r. $f ( x ) = x ^ { 3 } - 1 x ^ { 2 } - 14 x + 12 \quad k = 4$

Find real numbers a and b such that the equation is true. $a + b i = - 8 + 18 i$

Find all the real zeros of the polynomial function. $f ( x ) = x ^ { 2 } - 9$

Select the graph of the function $y = ( x / 3 ) ^ { 2 } - 3$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .

Graph the polynomial function. $y = - x ^ { 3 } + 3$

Solve the inequality and graph the solution on the real number line. $9 x ^ { 2 } - 6 x + 1 \leq 0$

Let $P ( x ) = 2 x ^ { 3 } + 9 x ^ { 2 } - 7 x + 3$ . Use synthetic division to find the value P (-7).

The graph of the function $f ( x ) = \frac { 3 x } { x ^ { 2 } - 4 }$ is shown below.Determine the domain. $The graph of the function f ( x ) = \frac { 3 x } { x ^ { 2 } - 4 } is shown below.Determine the domain.$

Find the domain of x in the expression. $\sqrt { \frac { x } { x ^ { 2 } - 2 x - 24 } }$

Select the graph of the function $y = \frac { 3 } { 2 } x ^ { 2 }$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .