Question 1

Give the equations of any vertical asymptotes.
-$$h ( x ) = \frac { 5 } { x - 5 }$$

Accepted Answer

A)  none 
B)  $x = - 5$ 
C)  $y = 5$ 
D)  $x = 5$ 
A)  none 
B)  $x = - 5$ 
C)  $y = 5$ 
D)  $x = 5$

Question 2

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given.
-$f ( x ) = 3 x ^ { 3 } - 3 x + 8 ; - 2$ and $- 1$

Accepted Answer

A)  $f ( - 2 ) = - 10$ and $f ( - 1 ) = 8$ 
B)  $f ( - 2 ) = - 9$ and $f ( - 1 ) = 9$ 
C)  $f ( - 2 ) = 10$ and $f ( - 1 ) = - 8$ 
D)  $f ( - 2 ) = 10$ and $f ( - 1 ) = 8$ 
A)  $f ( - 2 ) = - 10$ and $f ( - 1 ) = 8$ 
B)  $f ( - 2 ) = - 9$ and $f ( - 1 ) = 9$ 
C)  $f ( - 2 ) = 10$ and $f ( - 1 ) = - 8$ 
D)  $f ( - 2 ) = 10$ and $f ( - 1 ) = 8$

Question 3

Use the remainder theorem and synthetic division to find f(k).
-$k = 1 ; f ( x ) = 5 x ^ { 5 } + 2 x ^ { 3 } - 5 x ^ { 2 } - 3$

Accepted Answer

A)   -15 
B)   -9 
C)   -1 
D)  0 
A)   -15 
B)   -9 
C)   -1 
D)  0

Question 4

A piece of cardboard is twice as long as it is wide. It is to be made into a box with an open top by cutting 5 cm squares from each corner and folding up the sides. Let x represent the width of the original piece of cardboard.
Determine a function V that represents the volume of the box in terms of x.

Accepted Answer

A)  $V ( x ) = 10 x ^ { 2 } - 75 x + 125$ 
B)  $V ( x ) = 10 x ^ { 2 }$ 
C)  $V ( x ) = 5 x ^ { 2 } - 100 x + 500$ 
D)  $V ( x ) = 10 x ^ { 2 } - 150 x + 500$ 
A)  $V ( x ) = 10 x ^ { 2 } - 75 x + 125$ 
B)  $V ( x ) = 10 x ^ { 2 }$ 
C)  $V ( x ) = 5 x ^ { 2 } - 100 x + 500$ 
D)  $V ( x ) = 10 x ^ { 2 } - 150 x + 500$

Question 5

Find an equation for the rational function graph.
-

Accepted Answer

A)  $f ( x ) = \frac { - 1 } { x ^ { 2 } - 5 }$ 
B)  $f ( x ) = \frac { - 1 } { x ^ { 2 } + 5 }$ 
C)  $f ( x ) = \frac { - 1 } { x ^ { 2 } - 1 }$ 
D)  $f ( x ) = \frac { - 1 } { x ^ { 2 } + 1 }$ 
A)  $f ( x ) = \frac { - 1 } { x ^ { 2 } - 5 }$ 
B)  $f ( x ) = \frac { - 1 } { x ^ { 2 } + 5 }$ 
C)  $f ( x ) = \frac { - 1 } { x ^ { 2 } - 1 }$ 
D)  $f ( x ) = \frac { - 1 } { x ^ { 2 } + 1 }$

Question 6

Find the equation that the given graph represents.
-

Accepted Answer

A)  $P ( x ) = - x ^ { 6 } + 7 x ^ { 5 } - x ^ { 2 } - 2 x + 16$ 
B)  $P ( x ) = - 2 x ^ { 5 } + 7 x ^ { 4 } + 9 x ^ { 3 } - 40 x ^ { 2 } + 4 x + 16$ 
C)  $P ( x ) = 2 x ^ { 6 } + 9 x ^ { 3 } - 7 x ^ { 2 } + 4 x - 16$ 
D)  $P ( x ) = x ^ { 5 } + 7 x ^ { 4 } - x ^ { 3 } - 40 x ^ { 2 } + 2 x + 16$ 
A)  $P ( x ) = - x ^ { 6 } + 7 x ^ { 5 } - x ^ { 2 } - 2 x + 16$ 
B)  $P ( x ) = - 2 x ^ { 5 } + 7 x ^ { 4 } + 9 x ^ { 3 } - 40 x ^ { 2 } + 4 x + 16$ 
C)  $P ( x ) = 2 x ^ { 6 } + 9 x ^ { 3 } - 7 x ^ { 2 } + 4 x - 16$ 
D)  $P ( x ) = x ^ { 5 } + 7 x ^ { 4 } - x ^ { 3 } - 40 x ^ { 2 } + 2 x + 16$

Question 7

Sketch the graph of the parabola.
-$$y = x ^ { 2 } + 3$$

Accepted Answer

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

Question 8

For the polynomial, one zero is given. Find all others.
-$$P ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 23 x ^ { 2 } - 10 x + 22 ; i$$

Accepted Answer

A)  $- i , 5 + 2 \sqrt { 3 } , 5 - 2 \sqrt { 3 }$ 
B)  $- i , 1 + \sqrt { 3 } , 1 - \sqrt { 3 }$ 
C)  $- i , - 5 + \sqrt { 3 } , - 5 - \sqrt { 3 }$ 
D)  $- i , 5 + \sqrt { 3 } , 5 - \sqrt { 3 }$ 
A)  $- i , 5 + 2 \sqrt { 3 } , 5 - 2 \sqrt { 3 }$ 
B)  $- i , 1 + \sqrt { 3 } , 1 - \sqrt { 3 }$ 
C)  $- i , - 5 + \sqrt { 3 } , - 5 - \sqrt { 3 }$ 
D)  $- i , 5 + \sqrt { 3 } , 5 - \sqrt { 3 }$

Question 9

Provide an appropriate response.
-For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } + 4 x + 5$ have two $x$-intercepts?

Accepted Answer

A)  $a  \frac { 4 } { 5 }$ 
D)  a $> \frac { 16 } { 5 }$ 
A)  $a  \frac { 4 } { 5 }$ 
D)  a $> \frac { 16 } { 5 }$

Question 10

Solve the problem. Round your answer to two decimal places.
-The period of vibration P for a pendulum varies directly as the square root of the length L. If the period of vibration is 3 sec when the length is 36 inches, what is the period when $$\mathrm { L } = 2.25 \text { inches }$$

Accepted Answer

A)  3.5 sec 
B)  3.25 sec 
C)  3.75 sec 
D)  0.75 sec 
A)  3.5 sec 
B)  3.25 sec 
C)  3.75 sec 
D)  0.75 sec

Question 11

Find the zeros of the polynomial function and state the multiplicity of each.
-$$f ( x ) = 4 x ( x - 8 ) ( x + 10 )$$

Accepted Answer

A)  $- 10$ (multiplicity 1), 8 (multiplicity 1) 
B)  -10 (multiplicity 1), 0 (multiplicity 1), 8 (multiplicity 1) 
C)  $- 10$ (multiplicity 1) 8 (multiplicity 2) 
D)  $- 10$ (multiplicity 1), 10 (multiplicity 1), 8 (multiplicity 1) 
A)  $- 10$ (multiplicity 1), 8 (multiplicity 1) 
B)  -10 (multiplicity 1), 0 (multiplicity 1), 8 (multiplicity 1) 
C)  $- 10$ (multiplicity 1) 8 (multiplicity 2) 
D)  $- 10$ (multiplicity 1), 10 (multiplicity 1), 8 (multiplicity 1)

Question 12

Use the equation and the corresponding graph for the quadratic function to find what is requested.
-$f(x)=(x-3)^{2}-6$

Find the $y$-intercept.

Accepted Answer

A)  $( 0,4 )$ 
B)  $( 3,0 )$ 
C)  $( 0,3 )$ 
D)  $( - 3,0 )$ 
A)  $( 0,4 )$ 
B)  $( 3,0 )$ 
C)  $( 0,3 )$ 
D)  $( - 3,0 )$

Question 13

A rectangular piece of cardboard measuring 30 inches by 36 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each
Such square. What is the maximum volume of this box? If necessary, round to 2 decimal places.

Accepted Answer

A)  36,381.59 in3 
B)  148.81 in3 
C)  1155.68 in3 
D)  2612.81 in3 
A)  36,381.59 in3 
B)  148.81 in3 
C)  1155.68 in3 
D)  2612.81 in3

Question 14

The data in the table show the number of burglaries reported in a small town for several years on record.

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

Accepted Answer

A)  $f ( x ) = 0.001 x ^ { 3 } + 0.03 x ^ { 2 } - 0.93 x + 7.78$ 
B)  $f ( x ) = 0.0003 x ^ { 3 } + 0.01 x ^ { 2 } - 0.07 x + 7.68$ 
C)  $f ( x ) = - 0.0003 x ^ { 4 } + 0.01 x ^ { 3 } - 0.07 x ^ { 2 } - 0.65 x + 7.68$ 
D)  $f ( x ) = - 0.31 x + 6.15$ 
A)  $f ( x ) = 0.001 x ^ { 3 } + 0.03 x ^ { 2 } - 0.93 x + 7.78$ 
B)  $f ( x ) = 0.0003 x ^ { 3 } + 0.01 x ^ { 2 } - 0.07 x + 7.68$ 
C)  $f ( x ) = - 0.0003 x ^ { 4 } + 0.01 x ^ { 3 } - 0.07 x ^ { 2 } - 0.65 x + 7.68$ 
D)  $f ( x ) = - 0.31 x + 6.15$

Question 15

Find the equation that the given graph represents.
-

Accepted Answer

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

Question 16

John owns a hotdog stand. His profit is represented by the equation $P ( x ) = - x ^ { 2 } + 14 x + 54$ with P being profits and x the number of hotdogs sold. What is the most he can earn?

Accepted Answer

A)  $103 
B)  $75 
C)  $117 
D)  $49 
A)  $103 
B)  $75 
C)  $117 
D)  $49

Question 17

Find the zeros of the polynomial function and state the multiplicity of each.
$f ( x ) = \left( x ^ { 2 } + 12 x + 32 \right) ^ { 2 }$

Accepted Answer

A)  8 (multiplicity 2), 4 (multiplicity 2) 
B)  2 (multiplicity 2),  -2  (multiplicity 2) 
C)   -2  (multiplicity 4) 
D)   -4  (multiplicity 2),  -8  (multiplicity 2) 
A)  8 (multiplicity 2), 4 (multiplicity 2) 
B)  2 (multiplicity 2),  -2  (multiplicity 2) 
C)   -2  (multiplicity 4) 
D)   -4  (multiplicity 2),  -8  (multiplicity 2)

Give the equations of any vertical asymptotes. - $h ( x ) = \frac { 5 } { x - 5 }$

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = 3 x ^ { 3 } - 3 x + 8 ; - 2$ and $- 1$

Use the remainder theorem and synthetic division to find f(k). - $k = 1 ; f ( x ) = 5 x ^ { 5 } + 2 x ^ { 3 } - 5 x ^ { 2 } - 3$

Find an equation for the rational function graph. -

Find the equation that the given graph represents. -

Sketch the graph of the parabola. - $y = x ^ { 2 } + 3$ $Sketch the graph of the parabola. - y = x ^ { 2 } + 3$

For the polynomial, one zero is given. Find all others. - $P ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 23 x ^ { 2 } - 10 x + 22 ; i$

Provide an appropriate response. -For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } + 4 x + 5$ have two $x$ -intercepts?

Solve the problem. Round your answer to two decimal places. -The period of vibration P for a pendulum varies directly as the square root of the length L. If the period of vibration is 3 sec when the length is 36 inches, what is the period when $\mathrm { L } = 2.25 \text { inches }$

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 4 x ( x - 8 ) ( x + 10 )$

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=(x-3)^{2}-6$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=(x-3)^{2}-6 Find the y -intercept.$ Find the $y$ -intercept.

The data in the table show the number of burglaries reported in a small town for several years on record. Determine the linear, quadratic, cubic, or quartic function that best fits the data.

Find the equation that the given graph represents. -

John owns a hotdog stand. His profit is represented by the equation $P ( x ) = - x ^ { 2 } + 14 x + 54$ with P being profits and x the number of hotdogs sold. What is the most he can earn?

Find the zeros of the polynomial function and state the multiplicity of each. $f ( x ) = \left( x ^ { 2 } + 12 x + 32 \right) ^ { 2 }$

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

Give the equations of any vertical asymptotes. - h(x)=5x−5h ( x ) = \frac { 5 } { x - 5 }h(x)=x−55​

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - f(x)=3x3−3x+8;−2f ( x ) = 3 x ^ { 3 } - 3 x + 8 ; - 2f(x)=3x3−3x+8;−2 and −1- 1−1

Use the remainder theorem and synthetic division to find f(k). - k=1;f(x)=5x5+2x3−5x2−3k = 1 ; f ( x ) = 5 x ^ { 5 } + 2 x ^ { 3 } - 5 x ^ { 2 } - 3k=1;f(x)=5x5+2x3−5x2−3

Find an equation for the rational function graph. -

Find the equation that the given graph represents. -

Sketch the graph of the parabola. - y=x2+3y = x ^ { 2 } + 3y=x2+3

For the polynomial, one zero is given. Find all others. - P(x)=x4−10x3+23x2−10x+22;iP ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 23 x ^ { 2 } - 10 x + 22 ; iP(x)=x4−10x3+23x2−10x+22;i

Provide an appropriate response. -For what values of a does the quadratic function f(x)=ax2+4x+5f ( x ) = a x ^ { 2 } + 4 x + 5f(x)=ax2+4x+5 have two xxx -intercepts?

Find the zeros of the polynomial function and state the multiplicity of each. - f(x)=4x(x−8)(x+10)f ( x ) = 4 x ( x - 8 ) ( x + 10 )f(x)=4x(x−8)(x+10)

Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=(x−3)2−6f(x)=(x-3)^{2}-6f(x)=(x−3)2−6 Find the yyy -intercept.

The data in the table show the number of burglaries reported in a small town for several years on record. Determine the linear, quadratic, cubic, or quartic function that best fits the data.

Find the equation that the given graph represents. -

John owns a hotdog stand. His profit is represented by the equation P(x)=−x2+14x+54P ( x ) = - x ^ { 2 } + 14 x + 54P(x)=−x2+14x+54 with P being profits and x the number of hotdogs sold. What is the most he can earn?

Find the zeros of the polynomial function and state the multiplicity of each. f(x)=(x2+12x+32)2f ( x ) = \left( x ^ { 2 } + 12 x + 32 \right) ^ { 2 }f(x)=(x2+12x+32)2

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

Give the equations of any vertical asymptotes. - $h ( x ) = \frac { 5 } { x - 5 }$

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = 3 x ^ { 3 } - 3 x + 8 ; - 2$ and $- 1$

Use the remainder theorem and synthetic division to find f(k). - $k = 1 ; f ( x ) = 5 x ^ { 5 } + 2 x ^ { 3 } - 5 x ^ { 2 } - 3$

Sketch the graph of the parabola. - $y = x ^ { 2 } + 3$ $Sketch the graph of the parabola. - y = x ^ { 2 } + 3$

For the polynomial, one zero is given. Find all others. - $P ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 23 x ^ { 2 } - 10 x + 22 ; i$

Provide an appropriate response. -For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } + 4 x + 5$ have two $x$ -intercepts?

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 4 x ( x - 8 ) ( x + 10 )$

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=(x-3)^{2}-6$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=(x-3)^{2}-6 Find the y -intercept.$ Find the $y$ -intercept.

John owns a hotdog stand. His profit is represented by the equation $P ( x ) = - x ^ { 2 } + 14 x + 54$ with P being profits and x the number of hotdogs sold. What is the most he can earn?

Find the zeros of the polynomial function and state the multiplicity of each. $f ( x ) = \left( x ^ { 2 } + 12 x + 32 \right) ^ { 2 }$