Question 1

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zeros of $- 2,1,0$ and $\mathrm { P } ( 2 ) = 32$

Accepted Answer

A)  $P ( x ) = 4 x ^ { 3 } + 4 x ^ { 2 } - 8 x$ 
B)  $P ( x ) = 4 x ^ { 3 } - 4 x ^ { 2 } - 8 x$ 
C)  $P ( x ) = 4 x ^ { 3 } + 12 x ^ { 2 } - 8 x$ 
D)  $P ( x ) = 4 x ^ { 2 } + 4 x - 8$ 
A)  $P ( x ) = 4 x ^ { 3 } + 4 x ^ { 2 } - 8 x$ 
B)  $P ( x ) = 4 x ^ { 3 } - 4 x ^ { 2 } - 8 x$ 
C)  $P ( x ) = 4 x ^ { 3 } + 12 x ^ { 2 } - 8 x$ 
D)  $P ( x ) = 4 x ^ { 2 } + 4 x - 8$

Question 2

Give the domain and range for the rational function. Use interval notation.
-$$f ( x ) = \frac { 2 } { x } + 3$$

Accepted Answer

A)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; Range: $( - \infty , 3 ) \cup ( 3 , \infty )$ 
B)  Domain: $( - \infty , 2 ) \cup ( 2 , \infty )$; Range: $( - \infty , 3 ) \cup ( 3 , \infty )$ 
C)  Domain: $( - \infty , 3 ) \cup ( 3 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; Range: $( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
A)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; Range: $( - \infty , 3 ) \cup ( 3 , \infty )$ 
B)  Domain: $( - \infty , 2 ) \cup ( 2 , \infty )$; Range: $( - \infty , 3 ) \cup ( 3 , \infty )$ 
C)  Domain: $( - \infty , 3 ) \cup ( 3 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; Range: $( - \infty , - 3 ) \cup ( - 3 , \infty )$

Question 3

Answer the question
-$$\text { How can the graph of } f ( x ) = \frac { 1 } { x - 4 } + 6 \text { be obtained from the graph of } y = \frac { 1 } { x } ?$$

Accepted Answer

A)  By making a horizontal shift of 4 units to the right and a vertical shift of 6 units up 
B)  By making a horizontal shift of 4 units to the left and a vertical shift of 6 units up 
C)  By making a horizontal shift of 6 units to the right and a vertical shift of 4 units up 
D)  By making a horizontal shift of 6 units to the left and a vertical shift of 4 units down 
A)  By making a horizontal shift of 4 units to the right and a vertical shift of 6 units up 
B)  By making a horizontal shift of 4 units to the left and a vertical shift of 6 units up 
C)  By making a horizontal shift of 6 units to the right and a vertical shift of 4 units up 
D)  By making a horizontal shift of 6 units to the left and a vertical shift of 4 units down

Question 4

Determine which of the rational functions given below has the following feature(s).
-$x$-intercepts: $( - 4,0 )$ and $( 1,0 ) , y$-intercept: $\left( 0 , - \frac { 4 } { 3 } \right)$, vertical asymptotes: $x = - 1$ and $x = - 3$ horizontal asymptote: $\mathrm { y } = 1$

Accepted Answer

A)  $f ( x ) = \frac { ( x - 1 ) ( x - 3 ) } { ( x - 4 ) ( x + 1 ) }$ 
B)  $f ( x ) = \frac { ( x + 1 ) ( x + 3 ) } { ( x + 4 ) ( x - 1 ) }$ 
C)  $f ( x ) = \frac { ( x + 4 ) ( x - 1 ) } { ( x + 1 ) ( x + 3 ) }$ 
D)  $f ( x ) = \frac { ( x - 4 ) ( x + 1 ) } { ( x - 1 ) ( x - 3 ) }$ 
A)  $f ( x ) = \frac { ( x - 1 ) ( x - 3 ) } { ( x - 4 ) ( x + 1 ) }$ 
B)  $f ( x ) = \frac { ( x + 1 ) ( x + 3 ) } { ( x + 4 ) ( x - 1 ) }$ 
C)  $f ( x ) = \frac { ( x + 4 ) ( x - 1 ) } { ( x + 1 ) ( x + 3 ) }$ 
D)  $f ( x ) = \frac { ( x - 4 ) ( x + 1 ) } { ( x - 1 ) ( x - 3 ) }$

Question 5

Translate the given formula to an English phrase using the word "varies".
-P = nb, where P is the perimeter of a regular polygon with n sides each of length b.

Accepted Answer

The perimeter of a regular pol

Question 6

Use the graph to answer the question.
-Find the horizontal and vertical asymptotes of the rational function graphed below.

Accepted Answer

A)  Horizontal: $y = \pm 4$; vertical: $x = - 3$ 
B)  Horizontal: $y = 0$; vertical: $x = \pm 4$ 
C)  Horizontal: none; vertical: $x = \pm 4$ 
D)  Horizontal: $\mathrm { y } = - 3$; vertical: $\mathrm { x } = \pm 4$ 
A)  Horizontal: $y = \pm 4$; vertical: $x = - 3$ 
B)  Horizontal: $y = 0$; vertical: $x = \pm 4$ 
C)  Horizontal: none; vertical: $x = \pm 4$ 
D)  Horizontal: $\mathrm { y } = - 3$; vertical: $\mathrm { x } = \pm 4$

Question 7

Use the graph to answer the question.
-Find the horizontal and vertical asymptotes of the rational function graphed below.

Accepted Answer

A)  Horizontal: $\mathrm { y } = - 1$; vertical: none 
B)  Horizontal: $y = - 2$; vertical: $x = - 1$ 
C)  Horizontal: none; vertical: $x = - 2$ 
D)  Horizontal: $y = - 1$; vertical: $x = - 2$ 
A)  Horizontal: $\mathrm { y } = - 1$; vertical: none 
B)  Horizontal: $y = - 2$; vertical: $x = - 1$ 
C)  Horizontal: none; vertical: $x = - 2$ 
D)  Horizontal: $y = - 1$; vertical: $x = - 2$

Question 8

Find a polynomial of least degree with only real coefficients and having the given zeros.
-$- \sqrt { 6 } , \sqrt { 6 }$, and $- 7 i$

Accepted Answer

A)  $f ( x ) = x ^ { 4 } + 43 x ^ { 2 } - 294$ 
B)  $f ( x ) = x ^ { 4 } + 86 x ^ { 2 } + 294$ 
C)  $f ( x ) = x ^ { 4 } - 43 x ^ { 2 } - 294$ 
D)  $f ( x ) = x ^ { 4 } - 86 x ^ { 2 } + 294$ 
A)  $f ( x ) = x ^ { 4 } + 43 x ^ { 2 } - 294$ 
B)  $f ( x ) = x ^ { 4 } + 86 x ^ { 2 } + 294$ 
C)  $f ( x ) = x ^ { 4 } - 43 x ^ { 2 } - 294$ 
D)  $f ( x ) = x ^ { 4 } - 86 x ^ { 2 } + 294$

Question 9

Translate the given formula to an English phrase using the word "varies".
-Suppose $z$ varies directly as the square of $x$ and inversely as $y$. If $x$ is halved and $y$ is tripled, what happens to $\mathrm { z }$ ?

Accepted Answer

A)  $\mathrm { z }$ is six times as large as before 
B)  $z$ is one-twelfth as large as before 
C)  $\mathrm { z }$ is one-sixth as large as before 
D)  $\mathrm { z }$ is multiplied by $\frac { 3 } { 2 }$ 
A)  $\mathrm { z }$ is six times as large as before 
B)  $z$ is one-twelfth as large as before 
C)  $\mathrm { z }$ is one-sixth as large as before 
D)  $\mathrm { z }$ is multiplied by $\frac { 3 } { 2 }$

Question 10

Sketch the graph of the rational function.
-$$f ( x ) = \frac { 5 x } { ( x - 5 ) ( x + 4 ) }$$

Accepted Answer

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

Question 11

Round your answer to two decimal places.
-The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 52 miles
Per hour?

Accepted Answer

A)  201.58 ft 
B)  162.24 ft 
C)  189.62 ft 
D)  189.28 ft 
A)  201.58 ft 
B)  162.24 ft 
C)  189.62 ft 
D)  189.28 ft

Question 12

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

Question 13

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

Accepted Answer

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

Question 14

Round your answer to two decimal places.
-The distance an object falls when dropped from a tower varies directly as the square of the time it falls. If the object falls 144 feet in 3 seconds, how far will it fall in 17 seconds?

Accepted Answer

A)  272 ft 
B)  4624 ft 
C)  5202 ft 
D)  4046 ft 
A)  272 ft 
B)  4624 ft 
C)  5202 ft 
D)  4046 ft

Question 15

Find the correct end behavior diagram for the given polynomial function.
-$$P ( x ) = - x ^ { 5 } - 4 x ^ { 3 } - 5 x + 9$$

Accepted Answer

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

Question 16

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the
numbers given.
-$f ( x ) = 2 x ^ { 4 } - 10 x ^ { 2 } + 6 ; 2$ and 3

Accepted Answer

A)  $f ( 2 ) = - 1$ and $f ( 3 ) = 79$ 
B)  $f ( 2 ) = 2$ and $f ( 3 ) = 78$ 
C)  $f ( 2 ) = 2$ and $f ( 3 ) = - 78$ 
D)  $f ( 2 ) = - 2$ and $f ( 3 ) = 78$ 
A)  $f ( 2 ) = - 1$ and $f ( 3 ) = 79$ 
B)  $f ( 2 ) = 2$ and $f ( 3 ) = 78$ 
C)  $f ( 2 ) = 2$ and $f ( 3 ) = - 78$ 
D)  $f ( 2 ) = - 2$ and $f ( 3 ) = 78$

Question 17

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

Accepted Answer

A)  -9 
B)  -8 
C)  -1 
D)  3 
A)  -9 
B)  -8 
C)  -1 
D)  3

Question 18

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

Accepted Answer

A)  Domain: $( - \infty , - 2 ) \cup ( - 2 , \infty )$; Range: $( 0 , \infty )$ 
B)  Domain: $( - \infty , - 2 ) \cup ( - 2 , \infty )$; Range: $( 1 , \infty )$ 
C)  Domain: $( - 2 , \infty )$; Range: $( 0 , \infty )$ 
D)  Domain: $( - \infty , - 2 ) \cup ( - 2 , \infty )$; Range: $( - \infty , \infty )$ 
A)  Domain: $( - \infty , - 2 ) \cup ( - 2 , \infty )$; Range: $( 0 , \infty )$ 
B)  Domain: $( - \infty , - 2 ) \cup ( - 2 , \infty )$; Range: $( 1 , \infty )$ 
C)  Domain: $( - 2 , \infty )$; Range: $( 0 , \infty )$ 
D)  Domain: $( - \infty , - 2 ) \cup ( - 2 , \infty )$; Range: $( - \infty , \infty )$

Question 19

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.
-

Accepted Answer

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

Question 20

Translate the given formula to an English phrase using the word "varies".
-If m varies directly as p, and m = 63 when p = 9, find m when p is 6.

Accepted Answer

A)  36 
B)  49 
C)  42 
D)  81 
A)  36 
B)  49 
C)  42 
D)  81

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $- 2,1,0$ and $\mathrm { P } ( 2 ) = 32$

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = \frac { 2 } { x } + 3$

Answer the question - $\text { How can the graph of } f ( x ) = \frac { 1 } { x - 4 } + 6 \text { be obtained from the graph of } y = \frac { 1 } { x } ?$

Determine which of the rational functions given below has the following feature(s). - $x$ -intercepts: $( - 4,0 )$ and $( 1,0 ) , y$ -intercept: $\left( 0 , - \frac { 4 } { 3 } \right)$ , vertical asymptotes: $x = - 1$ and $x = - 3$ horizontal asymptote: $\mathrm { y } = 1$

Translate the given formula to an English phrase using the word "varies". -P = nb, where P is the perimeter of a regular polygon with n sides each of length b.

Use the graph to answer the question. -Find the horizontal and vertical asymptotes of the rational function graphed below.

Use the graph to answer the question. -Find the horizontal and vertical asymptotes of the rational function graphed below.

Find a polynomial of least degree with only real coefficients and having the given zeros. - $- \sqrt { 6 } , \sqrt { 6 }$ , and $- 7 i$

Translate the given formula to an English phrase using the word "varies". -Suppose $z$ varies directly as the square of $x$ and inversely as $y$ . If $x$ is halved and $y$ is tripled, what happens to $\mathrm { z }$ ?

Sketch the graph of the rational function. - $f ( x ) = \frac { 5 x } { ( x - 5 ) ( x + 4 ) }$ $Sketch the graph of the rational function. - f ( x ) = \frac { 5 x } { ( x - 5 ) ( x + 4 ) }$

Round your answer to two decimal places. -The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 52 miles Per hour?

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

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

Round your answer to two decimal places. -The distance an object falls when dropped from a tower varies directly as the square of the time it falls. If the object falls 144 feet in 3 seconds, how far will it fall in 17 seconds?

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = - x ^ { 5 } - 4 x ^ { 3 } - 5 x + 9$

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = 2 x ^ { 4 } - 10 x ^ { 2 } + 6 ; 2$ and 3

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

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

Translate the given formula to an English phrase using the word "varies". -If m varies directly as p, and m = 63 when p = 9, find m when p is 6.

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 of degree 3 with real coefficients that satisfies the given conditions. -Zeros of −2,1,0- 2,1,0−2,1,0 and P(2)=32\mathrm { P } ( 2 ) = 32P(2)=32

Give the domain and range for the rational function. Use interval notation. - f(x)=2x+3f ( x ) = \frac { 2 } { x } + 3f(x)=x2​+3

Answer the question - How can the graph of f(x)=1x−4+6 be obtained from the graph of y=1x?\text { How can the graph of } f ( x ) = \frac { 1 } { x - 4 } + 6 \text { be obtained from the graph of } y = \frac { 1 } { x } ? How can the graph of f(x)=x−41​+6 be obtained from the graph of y=x1​?

Translate the given formula to an English phrase using the word "varies". -P = nb, where P is the perimeter of a regular polygon with n sides each of length b.

Use the graph to answer the question. -Find the horizontal and vertical asymptotes of the rational function graphed below.

Use the graph to answer the question. -Find the horizontal and vertical asymptotes of the rational function graphed below.

Find a polynomial of least degree with only real coefficients and having the given zeros. - −6,6- \sqrt { 6 } , \sqrt { 6 }−6​,6​ , and −7i- 7 i−7i

Translate the given formula to an English phrase using the word "varies". -Suppose zzz varies directly as the square of xxx and inversely as yyy . If xxx is halved and yyy is tripled, what happens to z\mathrm { z }z ?

Sketch the graph of the rational function. - f(x)=5x(x−5)(x+4)f ( x ) = \frac { 5 x } { ( x - 5 ) ( x + 4 ) }f(x)=(x−5)(x+4)5x​

Round your answer to two decimal places. -The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 52 miles Per hour?

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

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

Round your answer to two decimal places. -The distance an object falls when dropped from a tower varies directly as the square of the time it falls. If the object falls 144 feet in 3 seconds, how far will it fall in 17 seconds?

Find the correct end behavior diagram for the given polynomial function. - P(x)=−x5−4x3−5x+9P ( x ) = - x ^ { 5 } - 4 x ^ { 3 } - 5 x + 9P(x)=−x5−4x3−5x+9

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - f(x)=2x4−10x2+6;2f ( x ) = 2 x ^ { 4 } - 10 x ^ { 2 } + 6 ; 2f(x)=2x4−10x2+6;2 and 3

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

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

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 x2x ^ { 2 }x2 should be positive or negative. -

Translate the given formula to an English phrase using the word "varies". -If m varies directly as p, and m = 63 when p = 9, find m when p is 6.

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

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $- 2,1,0$ and $\mathrm { P } ( 2 ) = 32$

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = \frac { 2 } { x } + 3$

Answer the question - $\text { How can the graph of } f ( x ) = \frac { 1 } { x - 4 } + 6 \text { be obtained from the graph of } y = \frac { 1 } { x } ?$

Find a polynomial of least degree with only real coefficients and having the given zeros. - $- \sqrt { 6 } , \sqrt { 6 }$ , and $- 7 i$

Translate the given formula to an English phrase using the word "varies". -Suppose $z$ varies directly as the square of $x$ and inversely as $y$ . If $x$ is halved and $y$ is tripled, what happens to $\mathrm { z }$ ?

Sketch the graph of the rational function. - $f ( x ) = \frac { 5 x } { ( x - 5 ) ( x + 4 ) }$ $Sketch the graph of the rational function. - f ( x ) = \frac { 5 x } { ( x - 5 ) ( x + 4 ) }$

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

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

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = - x ^ { 5 } - 4 x ^ { 3 } - 5 x + 9$

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = 2 x ^ { 4 } - 10 x ^ { 2 } + 6 ; 2$ and 3

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