Question 1

Use the factor theorem to decide whether or not the second polynomial is a factor of the first.
-$3 x ^ { 2 } - 21 x + 36 ; x - 4$

Accepted Answer

A) True 
 B)False

Question 2

The price of electric guitars has varied considerably in recent years. The data in the table relates the price P, in dollars, to time t, in years. Use a cubic function fitted to the data to predict the price of an electric guitar in year 10. $$\begin{array} { c | c } 
\text { Year, } \mathrm { t } & \begin{array} { c } 
\text { Average price, } \mathrm { p } , \
\text { of an electric guitar }
\end{array} \
\hline 1 & \$ 618.20 \
\hline 2 & 783.20 \
\hline 3 & 674.30 \
\hline 4 & 721.60 \
\hline 5 & 825.00 \
\hline 6 & 891.00 \
\hline 7 & 852.50 \
\hline 8 & 819.50 \
\hline 9 & 783.20
\end{array}$$

Accepted Answer

A)  $893.53 
B)  $827.42 
C)  $443.52 
D)  $670.48 
A)  $893.53 
B)  $827.42 
C)  $443.52 
D)  $670.48

Question 3

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function.
-$$f ( x ) = 2 x ^ { 8 } + 4 x ^ { 6 } + 2 x ^ { 4 } + 7 x ^ { 2 } + 2$$

Accepted Answer

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

Question 4

Suppose z varies directly as x and inversely as the square of y. If x is doubled and y is tripled, what happens to z?

Accepted Answer

A)  $\mathrm { z }$ is one-sixth as large as before 
B)  $z$ is six times as large as before 
C)  $\mathrm { z }$ is multiplied by $\frac { 1 } { 18 }$ 
D)  $\mathrm { z }$ is multiplied by $\frac { 2 } { 9 }$ 
A)  $\mathrm { z }$ is one-sixth as large as before 
B)  $z$ is six times as large as before 
C)  $\mathrm { z }$ is multiplied by $\frac { 1 } { 18 }$ 
D)  $\mathrm { z }$ is multiplied by $\frac { 2 } { 9 }$

Question 5

Match the equation to the correct graph.
$y = \frac { 1 } { 3 } ( x - 5 ) ^ { 2 } + 6$

Accepted Answer

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

Question 6

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

Question 7

The table shows the population of a city over the past five years. $$\begin{array} { c | c } 
& \text { Population } \
\text { Year } & \text { (in millions of people) } \
\hline 0 & 65 \
1 & 65.5 \
2 & 67 \
3 & 69 \
4 & 71.5
\end{array}$$ We used this data to develop the quadratic function $f ( x ) = 0.373 x ^ { 2 } + 0.165 x + 65$ which models the population of the city y in millions in the year x. Use the model to find the estimated population in year 9.

Accepted Answer

A)  66,822,000 
B)  65,538,000 
C)  1,490,000 
D)  1,490,000,000,000 
A)  66,822,000 
B)  65,538,000 
C)  1,490,000 
D)  1,490,000,000,000

Question 8

The weight of a person on or above the surface of the earth varies inversely as the square of the distance the person is from the center of the earth. If a person weighs 180 pounds on the surface of the earth and the radius
Of the earth is 3900 miles, what will the person weigh if he or she is 150 miles above the earth's surface? Round
Your answer to the nearest hundredth of a pound.

Accepted Answer

A)  166.91 lb 
B)  166.41 lb 
C)  167.31 lb 
D)  168.31 lb 
A)  166.91 lb 
B)  166.41 lb 
C)  167.31 lb 
D)  168.31 lb

Question 9

Sketch the graph of the parabola.
-$$y = 4 x ^ { 2 } - 2 x - 8$$

Accepted Answer

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

Question 10

How many positive real zeros does this graph have?

Accepted Answer

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

Question 11

What type of variation is suggested by the graph?

Accepted Answer

A)  y varies directly as x 
B)  y varies directly as the square of x 
C)  y varies inversely as the square of x 
D)  y varies inversely as x 
A)  y varies directly as x 
B)  y varies directly as the square of x 
C)  y varies inversely as the square of x 
D)  y varies inversely as x

Question 12

A rock is propelled upward from the top of a building 270 feet tall at an initial velocity of 168 feet per second. The function that describes the height of the rocket in terms of time t is $( t ) = - 16 t ^ { 2 } + 168 t + 270$ Determine the
Time at which the rock reaches its maximum height.

Accepted Answer

A)  8.4 sec 
B)  10.5 sec 
C)  4.2 sec 
D)  5.25 sec 
A)  8.4 sec 
B)  10.5 sec 
C)  4.2 sec 
D)  5.25 sec

Question 13

For the polynomial, one zero is given. Find all others.
-$$P ( x ) = x ^ { 3 } - 7 x ^ { 2 } + 15 x - 25 ; 5$$

Accepted Answer

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

Question 14

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth.
-$$f ( x ) = x ^ { 4 } - 9 x ^ { 2 } + 20$$

Accepted Answer

A)  $- 1,2.7,2.7 , - 2.7$ 
B)  $2.2 , - 2.2,2 , - 2$ 
C)  $2.2,2$ 
D)  $5 , - 5,4 , - 4$ 
A)  $- 1,2.7,2.7 , - 2.7$ 
B)  $2.2 , - 2.2,2 , - 2$ 
C)  $2.2,2$ 
D)  $5 , - 5,4 , - 4$

Question 15

Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f.
-

Accepted Answer

A)  Vertical: $x = - 2 ;$ oblique: $y = x - 2 ; ( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
B)  Vertical: $x = - 2 ;$ oblique: $y = x + 2 ; ( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
C)  Vertical: $x = - 2 ;$ oblique: $y = x + 2 ; ( - \infty , 2 ) \cup ( 2 , \infty )$ 
D)  Vertical: $x = 2$; oblique: $y = x - 2 ; ( - \infty , 2 ) \cup ( 2 , \infty )$ 
A)  Vertical: $x = - 2 ;$ oblique: $y = x - 2 ; ( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
B)  Vertical: $x = - 2 ;$ oblique: $y = x + 2 ; ( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
C)  Vertical: $x = - 2 ;$ oblique: $y = x + 2 ; ( - \infty , 2 ) \cup ( 2 , \infty )$ 
D)  Vertical: $x = 2$; oblique: $y = x - 2 ; ( - \infty , 2 ) \cup ( 2 , \infty )$

Question 16

Find the zeros of the polynomial function and state the multiplicity of each.
$f ( x ) = 4 ( x + 4 ) ^ { 3 } ( x - 4 ) ( x - 4 + i )$

Accepted Answer

A)  4 (multiplicity 3),  -4  (multiplicity 1),  -4+i (multiplicity 1) 
B)  4 (multiplicity 3), 4 (multiplicity 1), 4 - i (multiplicity 1) 
C)   -4  (multiplicity 3),  -4  (multiplicity 1), 4 - i (multiplicity 1) 
D)   -4  (multiplicity 3), 4 (multiplicity 1),  4- i (multiplicity 1) 
A)  4 (multiplicity 3),  -4  (multiplicity 1),  -4+i (multiplicity 1) 
B)  4 (multiplicity 3), 4 (multiplicity 1), 4 - i (multiplicity 1) 
C)   -4  (multiplicity 3),  -4  (multiplicity 1), 4 - i (multiplicity 1) 
D)   -4  (multiplicity 3), 4 (multiplicity 1),  4- i (multiplicity 1)

Question 17

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.
-$$f ( x ) = x ^ { 3 } - 4 x - 1 ; [ 1,2 ]$$

Accepted Answer

A)  $( 1.15 , - 4.08 )$ 
B)  $( 4,47 )$ 
C)  $( - 1.15,2.08 )$ 
D)  $( 0 , - 1 )$ 
A)  $( 1.15 , - 4.08 )$ 
B)  $( 4,47 )$ 
C)  $( - 1.15,2.08 )$ 
D)  $( 0 , - 1 )$

Question 18

A coin is tossed upward from a balcony 200 feet high with an initial velocity of 48 feet per second, then its height after  t  seconds is given by the equation $h ( t ) = - 16 t ^ { 2 } + 48 t + 200$
During what interval of time will the coin be at a height of at least  40 ft?

Accepted Answer

A)  $0 \leq t \leq 5$ 
B)  $4 \leq t \leq 5$ 
C)  $0 \leq t \leq 1$ 
D)  $5 \leq t \leq 10$ 
A)  $0 \leq t \leq 5$ 
B)  $4 \leq t \leq 5$ 
C)  $0 \leq t \leq 1$ 
D)  $5 \leq t \leq 10$

Question 19

What are the possible numbers of real zeros (counting multiplicities) for a polynomial function with real coefficients of degree six?

Accepted Answer

A)  1, 3, or 5 
B)  0, 2, 4, or 6 
C)  2, 4, or 6 
D)  6 
A)  1, 3, or 5 
B)  0, 2, 4, or 6 
C)  2, 4, or 6 
D)  6

Question 20

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.

Accepted Answer

A)  $f ( x ) = 0.00001 x ^ { 3 } - 0.003 x ^ { 2 } + 0.14 x + 2.16$ 
B)  $f ( x ) = 0.002 x + 2.90$ 
C)  $f ( x ) = - 0.002 x ^ { 2 } + 0.12 x + 2.19$ 
D)  $f ( x ) = - 0.003 x ^ { 2 } + 0.12 x + 2.19$ 
A)  $f ( x ) = 0.00001 x ^ { 3 } - 0.003 x ^ { 2 } + 0.14 x + 2.16$ 
B)  $f ( x ) = 0.002 x + 2.90$ 
C)  $f ( x ) = - 0.002 x ^ { 2 } + 0.12 x + 2.19$ 
D)  $f ( x ) = - 0.003 x ^ { 2 } + 0.12 x + 2.19$

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $3 x ^ { 2 } - 21 x + 36 ; x - 4$

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function. - $f ( x ) = 2 x ^ { 8 } + 4 x ^ { 6 } + 2 x ^ { 4 } + 7 x ^ { 2 } + 2$

Suppose z varies directly as x and inversely as the square of y. If x is doubled and y is tripled, what happens to z?

Match the equation to the correct graph. $y = \frac { 1 } { 3 } ( x - 5 ) ^ { 2 } + 6$

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

Sketch the graph of the parabola. - $y = 4 x ^ { 2 } - 2 x - 8$ $Sketch the graph of the parabola. - y = 4 x ^ { 2 } - 2 x - 8$

How many positive real zeros does this graph have?

What type of variation is suggested by the graph?

A rock is propelled upward from the top of a building 270 feet tall at an initial velocity of 168 feet per second. The function that describes the height of the rocket in terms of time t is $( t ) = - 16 t ^ { 2 } + 168 t + 270$ Determine the Time at which the rock reaches its maximum height.

For the polynomial, one zero is given. Find all others. - $P ( x ) = x ^ { 3 } - 7 x ^ { 2 } + 15 x - 25 ; 5$

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - $f ( x ) = x ^ { 4 } - 9 x ^ { 2 } + 20$

Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f. -

Find the zeros of the polynomial function and state the multiplicity of each. $f ( x ) = 4 ( x + 4 ) ^ { 3 } ( x - 4 ) ( x - 4 + i )$

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. - $f ( x ) = x ^ { 3 } - 4 x - 1 ; [ 1,2 ]$

A coin is tossed upward from a balcony 200 feet high with an initial velocity of 48 feet per second, then its height after t seconds is given by the equation $h ( t ) = - 16 t ^ { 2 } + 48 t + 200$ During what interval of time will the coin be at a height of at least 40 ft?

What are the possible numbers of real zeros (counting multiplicities) for a polynomial function with real coefficients of degree six?

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.

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

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - 3x2−21x+36;x−43 x ^ { 2 } - 21 x + 36 ; x - 43x2−21x+36;x−4

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function. - f(x)=2x8+4x6+2x4+7x2+2f ( x ) = 2 x ^ { 8 } + 4 x ^ { 6 } + 2 x ^ { 4 } + 7 x ^ { 2 } + 2f(x)=2x8+4x6+2x4+7x2+2

Suppose z varies directly as x and inversely as the square of y. If x is doubled and y is tripled, what happens to z?

Match the equation to the correct graph. y=13(x−5)2+6y = \frac { 1 } { 3 } ( x - 5 ) ^ { 2 } + 6y=31​(x−5)2+6

Factor f(x) into linear factors given that k is a zero of f(x). - f(x)=2x3−3x2−5x+6;k=1f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } - 5 x + 6 ; k = 1f(x)=2x3−3x2−5x+6;k=1

Sketch the graph of the parabola. - y=4x2−2x−8y = 4 x ^ { 2 } - 2 x - 8y=4x2−2x−8

How many positive real zeros does this graph have?

What type of variation is suggested by the graph?

For the polynomial, one zero is given. Find all others. - P(x)=x3−7x2+15x−25;5P ( x ) = x ^ { 3 } - 7 x ^ { 2 } + 15 x - 25 ; 5P(x)=x3−7x2+15x−25;5

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - f(x)=x4−9x2+20f ( x ) = x ^ { 4 } - 9 x ^ { 2 } + 20f(x)=x4−9x2+20

Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f. -

Find the zeros of the polynomial function and state the multiplicity of each. f(x)=4(x+4)3(x−4)(x−4+i)f ( x ) = 4 ( x + 4 ) ^ { 3 } ( x - 4 ) ( x - 4 + i )f(x)=4(x+4)3(x−4)(x−4+i)

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)=x3−4x−1;[1,2]f ( x ) = x ^ { 3 } - 4 x - 1 ; [ 1,2 ]f(x)=x3−4x−1;[1,2]

What are the possible numbers of real zeros (counting multiplicities) for a polynomial function with real coefficients of degree six?

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.

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

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $3 x ^ { 2 } - 21 x + 36 ; x - 4$

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function. - $f ( x ) = 2 x ^ { 8 } + 4 x ^ { 6 } + 2 x ^ { 4 } + 7 x ^ { 2 } + 2$

Match the equation to the correct graph. $y = \frac { 1 } { 3 } ( x - 5 ) ^ { 2 } + 6$

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

Sketch the graph of the parabola. - $y = 4 x ^ { 2 } - 2 x - 8$ $Sketch the graph of the parabola. - y = 4 x ^ { 2 } - 2 x - 8$

For the polynomial, one zero is given. Find all others. - $P ( x ) = x ^ { 3 } - 7 x ^ { 2 } + 15 x - 25 ; 5$

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - $f ( x ) = x ^ { 4 } - 9 x ^ { 2 } + 20$

Find the zeros of the polynomial function and state the multiplicity of each. $f ( x ) = 4 ( x + 4 ) ^ { 3 } ( x - 4 ) ( x - 4 + i )$

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. - $f ( x ) = x ^ { 3 } - 4 x - 1 ; [ 1,2 ]$