Question 1

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k.
-$$f ( x ) = - 6 x ^ { 3 } + 2 x ^ { 2 } + 5 x - 10 ; \quad k = 2$$

Accepted Answer

A)  $f ( x ) = ( x + 2 ) \left( - 6 x ^ { 2 } + 10 x + 25 \right) - 40$ 
B)  $f ( x ) = ( x - 2 ) \left( - 6 x ^ { 2 } - 10 x + 15 \right) - 40$ 
C)  $f ( x ) = ( x - 2 ) \left( - 6 x ^ { 2 } - 10 x - 15 \right) - 40$ 
D)  $f ( x ) = ( x - 2 ) \left( - 6 x ^ { 2 } + 10 x + 25 \right) - 40$ 
A)  $f ( x ) = ( x + 2 ) \left( - 6 x ^ { 2 } + 10 x + 25 \right) - 40$ 
B)  $f ( x ) = ( x - 2 ) \left( - 6 x ^ { 2 } - 10 x + 15 \right) - 40$ 
C)  $f ( x ) = ( x - 2 ) \left( - 6 x ^ { 2 } - 10 x - 15 \right) - 40$ 
D)  $f ( x ) = ( x - 2 ) \left( - 6 x ^ { 2 } + 10 x + 25 \right) - 40$

Question 2

Solve the problem.
-Suppose the cost per ton, $y$, to build an oil platform of $x$ thousand tons is approximated by $f ( x ) = \frac { 312,500 } { x + 625 }$. What is the cost per ton for $x = 400$ ?

Accepted Answer

A)  $\$ 304.88$ 
B)  $\$ 121,951.22$ 
C)  $\$ 156.25$ 
D)  $\$ 200,000.00$ 
A)  $\$ 304.88$ 
B)  $\$ 121,951.22$ 
C)  $\$ 156.25$ 
D)  $\$ 200,000.00$

Question 3

Find the equation that the given graph represents.
-

Accepted Answer

A)  $P ( x ) = - x ^ { 5 } - 10 x ^ { 2 } - 10$ 
B)  $P ( x ) = x ^ { 4 } + x ^ { 3 } - 10 x ^ { 2 } + 10$ 
C)  $P ( x ) = - x ^ { 4 } + x ^ { 3 } - 12 x ^ { 2 } + 10$ 
D)  $P ( x ) = x ^ { 5 } - 4 x ^ { 3 } + 12 x ^ { 2 } + 10$ 
A)  $P ( x ) = - x ^ { 5 } - 10 x ^ { 2 } - 10$ 
B)  $P ( x ) = x ^ { 4 } + x ^ { 3 } - 10 x ^ { 2 } + 10$ 
C)  $P ( x ) = - x ^ { 4 } + x ^ { 3 } - 12 x ^ { 2 } + 10$ 
D)  $P ( x ) = x ^ { 5 } - 4 x ^ { 3 } + 12 x ^ { 2 } + 10$

Question 4

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k.
-$$f ( x ) = 2 x ^ { 5 } - x ^ { 4 } + 3 x ^ { 2 } - x + 5 ; \quad k = 1$$

Accepted Answer

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

Question 5

Answer the question
-How can the graph of $f ( x ) = \frac { 1 } { x - 3 }$ be obtained from the graph of $y = \frac { 1 } { x }$ ?

Accepted Answer

A)  By making a vertical shift of 3 units down 
B)  By making a horizontal shift of 3 units to the left 
C)  By making a horizontal shift of 3 units to the right 
D)  By making a vertical shift of 3 units up 
A)  By making a vertical shift of 3 units down 
B)  By making a horizontal shift of 3 units to the left 
C)  By making a horizontal shift of 3 units to the right 
D)  By making a vertical shift of 3 units up

Question 6

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

Accepted Answer

A)  $- 15$ 
B)  3 
C)  $- 7$ 
D)  $- 5$ 
A)  $- 15$ 
B)  3 
C)  $- 7$ 
D)  $- 5$

Question 7

Determine whether the statement is true or false.
-If f(x) is a polynomial and f(3) = 0, then x + 3 is a factor of f(x).

Accepted Answer

A) True 
 B)False

Question 8

Identify the vertex of the parabola.
-$$f ( x ) = - 7 x ^ { 2 }$$

Accepted Answer

A)  $( 0,0 )$ 
B)  $( 0 , - 7 )$ 
C)  $( - 7,0 )$ 
D)  $( 7,0 )$ 
A)  $( 0,0 )$ 
B)  $( 0 , - 7 )$ 
C)  $( - 7,0 )$ 
D)  $( 7,0 )$

Question 9

Determine which of the rational functions given below has the following feature(s).
-The vertical asymptote is $x = 3$

Accepted Answer

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

Question 10

Solve the problem.
-Suppose the cost per ton, $\mathrm { f } ( \mathrm { x } )$, to build an oil platform of $x$ thousand tons is approximated by $f ( x ) = \frac { 312,500 } { x + 625 }$. What is the cost per ton for $x = 10$ ?

Accepted Answer

A)  $\$ 50.00$ 
B)  $\$ 30,625.00$ 
C)  $\$ 31,250.00$ 
D)  $\$ 492.13$ 
A)  $\$ 50.00$ 
B)  $\$ 30,625.00$ 
C)  $\$ 31,250.00$ 
D)  $\$ 492.13$

Question 11

Solve the problem.
-If a rocket is propelled upward from ground level, its height in meters after $t$ seconds is given by $h ( t ) = - 9.8 t ^ { 2 } + 98 t$. During what interval of time will the rocket be higher than $235.2 \mathrm {~m}$ ?

Accepted Answer

A)  $6 < t < 8$ 
B)  $8 < t < 10$ 
C)  $0 < t < 4$ 
D)  $4 < t < 6$ 
A)  $6 < t < 8$ 
B)  $8 < t < 10$ 
C)  $0 < t < 4$ 
D)  $4 < t < 6$

Question 12

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

Accepted Answer

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

Question 13

Solve the problem.
-$x$ and $y$ are two positive numbers and $y$ is three greater than $x$. The product of the numbers is 270 . Find the smaller number, $x$.

Accepted Answer

A)  15 
B)  18 
C)  9 
D)  8 
A)  15 
B)  18 
C)  9 
D)  8

Question 14

Use synthetic division to decide whether the given number k is a zero of the given polynomial function.
-$$- \frac { 2 } { 3 } ; f ( x ) = - 3 x ^ { 4 } - 5 x ^ { 2 } - 4$$

Accepted Answer

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

Question 15

Determine whether the statement is true or false.
-$$\text { The function } f ( x ) = \frac { x + 1 } { x ^ { 2 } } \text { is an even function. }$$

Accepted Answer

A) True 
 B)False

Question 16

Give the equations of any vertical asymptotes.
-$$f ( x ) = \frac { x - 2 } { x ^ { 2 } + 9 x }$$

Accepted Answer

A)  $x = 2$ 
B)  $x = - 9$ 
C)  $x = 9$ 
D)  $x = 0 , x = - 9$ 
A)  $x = 2$ 
B)  $x = - 9$ 
C)  $x = 9$ 
D)  $x = 0 , x = - 9$

Question 17

Provide an appropriate response.
-What are the possible numbers of real zeros (counting multiplicities) for a polynomial function with real coefficients of degree six?

Accepted Answer

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

Question 18

Solve the problem. Round to the nearest tenth unless indicated otherwise.
-At a fixed temperature, the resistance R of a wire varies directly as the length l and inversely as the square of its diameter d. If the resistance is 0.8 ohm when the diameter is 1 mm and the length is
200 cm, what is the resistance when the diameter is 2 mm and the length is 1050 cm?

Accepted Answer

A)  210.0 ohm 
B)  262.5 ohm 
C)  1.1 ohm 
D)  2.1 ohm 
A)  210.0 ohm 
B)  262.5 ohm 
C)  1.1 ohm 
D)  2.1 ohm

Question 19

Solve the problem.
-A rock is propelled upward from the top of a building 230 feet tall at an initial velocity of 192 feet per second. The function that describes the height of the rocket in terms of time $t$ is $s ( t ) = - 16 t ^ { 2 } + 192 t + 230$. Determine the time at which the rock reaches its maximum height.

Accepted Answer

A)  $9.6 \mathrm { sec }$ 
B)  $4.8 \mathrm { sec }$ 
C)  $12 \mathrm { sec }$ 
D)  $6 \mathrm { sec }$ 
A)  $9.6 \mathrm { sec }$ 
B)  $4.8 \mathrm { sec }$ 
C)  $12 \mathrm { sec }$ 
D)  $6 \mathrm { sec }$

Question 20

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k.
-$$f ( x ) = 3 x ^ { 4 } - 2 x ^ { 3 } - 10 x ^ { 2 } + 15 ; \quad k = 2$$

Accepted Answer

A)  $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 4 \right) + 7$ 
B)  $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } + 4 x ^ { 2 } - 2 x + 11 \right) + 22$ 
C)  $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } + 4 x ^ { 2 } + 2 x + 4 \right) + 22$ 
D)  $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } - 4 x ^ { 2 } - 2 x - 4 \right) + 7$ 
A)  $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 4 \right) + 7$ 
B)  $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } + 4 x ^ { 2 } - 2 x + 11 \right) + 22$ 
C)  $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } + 4 x ^ { 2 } + 2 x + 4 \right) + 22$ 
D)  $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } - 4 x ^ { 2 } - 2 x - 4 \right) + 7$

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - $f ( x ) = - 6 x ^ { 3 } + 2 x ^ { 2 } + 5 x - 10 ; \quad k = 2$

Solve the problem. -Suppose the cost per ton, $y$ , to build an oil platform of $x$ thousand tons is approximated by $f ( x ) = \frac { 312,500 } { x + 625 }$ . What is the cost per ton for $x = 400$ ?

Find the equation that the given graph represents. -

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - $f ( x ) = 2 x ^ { 5 } - x ^ { 4 } + 3 x ^ { 2 } - x + 5 ; \quad k = 1$

Answer the question -How can the graph of $f ( x ) = \frac { 1 } { x - 3 }$ be obtained from the graph of $y = \frac { 1 } { x }$ ?

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

Determine whether the statement is true or false. -If f(x) is a polynomial and f(3) = 0, then x + 3 is a factor of f(x).

Identify the vertex of the parabola. - $f ( x ) = - 7 x ^ { 2 }$

Determine which of the rational functions given below has the following feature(s). -The vertical asymptote is $x = 3$

Solve the problem. -Suppose the cost per ton, $\mathrm { f } ( \mathrm { x } )$ , to build an oil platform of $x$ thousand tons is approximated by $f ( x ) = \frac { 312,500 } { x + 625 }$ . What is the cost per ton for $x = 10$ ?

Solve the problem. -If a rocket is propelled upward from ground level, its height in meters after $t$ seconds is given by $h ( t ) = - 9.8 t ^ { 2 } + 98 t$ . During what interval of time will the rocket be higher than $235.2 \mathrm {~m}$ ?

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

Solve the problem. - $x$ and $y$ are two positive numbers and $y$ is three greater than $x$ . The product of the numbers is 270 . Find the smaller number, $x$ .

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $- \frac { 2 } { 3 } ; f ( x ) = - 3 x ^ { 4 } - 5 x ^ { 2 } - 4$

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { x + 1 } { x ^ { 2 } } \text { is an even function. }$

Give the equations of any vertical asymptotes. - $f ( x ) = \frac { x - 2 } { x ^ { 2 } + 9 x }$

Provide an appropriate response. -What are the possible numbers of real zeros (counting multiplicities) for a polynomial function with real coefficients of degree six?

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - $f ( x ) = 3 x ^ { 4 } - 2 x ^ { 3 } - 10 x ^ { 2 } + 15 ; \quad k = 2$

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

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Exam 3: Polynomial and Rational Functions

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - f(x)=−6x3+2x2+5x−10;k=2f ( x ) = - 6 x ^ { 3 } + 2 x ^ { 2 } + 5 x - 10 ; \quad k = 2f(x)=−6x3+2x2+5x−10;k=2

Solve the problem. -Suppose the cost per ton, yyy , to build an oil platform of xxx thousand tons is approximated by f(x)=312,500x+625f ( x ) = \frac { 312,500 } { x + 625 }f(x)=x+625312,500​ . What is the cost per ton for x=400x = 400x=400 ?

Find the equation that the given graph represents. -

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - f(x)=2x5−x4+3x2−x+5;k=1f ( x ) = 2 x ^ { 5 } - x ^ { 4 } + 3 x ^ { 2 } - x + 5 ; \quad k = 1f(x)=2x5−x4+3x2−x+5;k=1

Answer the question -How can the graph of f(x)=1x−3f ( x ) = \frac { 1 } { x - 3 }f(x)=x−31​ be obtained from the graph of y=1xy = \frac { 1 } { x }y=x1​ ?

Use the remainder theorem and synthetic division to find f(k). - k=−2;f(x)=x2+3x+5\mathrm { k } = - 2 ; f ( x ) = x ^ { 2 } + 3 x + 5k=−2;f(x)=x2+3x+5