Question 1

Give the equatiosn of any horizontal asymptotes.
-$$g ( x ) = \frac { x + 5 } { x ^ { 2 } - 6 }$$

Accepted Answer

A)  $y = 1$ 
B)  $\mathrm { y } = 0$ 
C)  none 
D)  $y = 6$ 
A)  $y = 1$ 
B)  $\mathrm { y } = 0$ 
C)  none 
D)  $y = 6$

Question 2

Provide an appropriate response.
-For what value of $c$ does the quadratic function $f ( x ) = 3 x ^ { 2 } + 8 x + c$ have exactly one $x$-intercept?

Accepted Answer

A)  $- \frac { 2 } { 3 }$ 
B)  $\frac { 2 } { 3 }$ 
C)  $\frac { 16 } { 3 }$ 
D)  16 
A)  $- \frac { 2 } { 3 }$ 
B)  $\frac { 2 } { 3 }$ 
C)  $\frac { 16 } { 3 }$ 
D)  16

Question 3

Factor f(x) into linear factors given that k is a zero of f(x).
-$$f ( x ) = 8 x ^ { 3 } + 34 x ^ { 2 } + 27 x - 9 ; k = \frac { 1 } { 4 }$$

Accepted Answer

A)  $( 4 x - 1 ) ( 2 x - 3 ) ( x - 3 )$ 
B)  $( 4 x + 1 ) ( 2 x + 1 ) ( x - 9 )$ 
C)  $( 4 x - 1 ) ( 2 x + 3 ) ( x + 3 )$ 
D)  $( 4 x + 1 ) ( 2 x + 3 ) ( x - 3 )$ 
A)  $( 4 x - 1 ) ( 2 x - 3 ) ( x - 3 )$ 
B)  $( 4 x + 1 ) ( 2 x + 1 ) ( x - 9 )$ 
C)  $( 4 x - 1 ) ( 2 x + 3 ) ( x + 3 )$ 
D)  $( 4 x + 1 ) ( 2 x + 3 ) ( x - 3 )$

Question 4

Answer the question
-How can the graph of $f ( x ) = \frac { 1 } { ( x - 5 ) ^ { 2 } } + 6$ be obtained from the graph of $y = \frac { 1 } { x ^ { 2 } } ?$

Accepted Answer

A)  By making a horizontal shift of 5 units to the left and a vertical shift of 6 units down 
B)  By making a horizontal shift of 5 units to the right and a vertical shift of 6 units up 
C)  By making a horizontal shift of 6 units to the left and a vertical shift of 5 units up 
D)  By making a horizontal shift of 6 units to the right and a vertical shift of 5 units down 
A)  By making a horizontal shift of 5 units to the left and a vertical shift of 6 units down 
B)  By making a horizontal shift of 5 units to the right and a vertical shift of 6 units up 
C)  By making a horizontal shift of 6 units to the left and a vertical shift of 5 units up 
D)  By making a horizontal shift of 6 units to the right and a vertical shift of 5 units down

Question 5

Find an equation for the rational function graph.
-

Accepted Answer

A)  $f ( x ) = \frac { x ( x + 6 ) } { x + 7 }$ 
B)  $f ( x ) = \frac { x ( x + 7 ) } { x + 6 }$ 
C)  $f ( x ) = \frac { x + 7 } { x ( x + 6 ) }$ 
D)  $f ( x ) = \frac { x + 6 } { x ( x + 7 ) }$ 
A)  $f ( x ) = \frac { x ( x + 6 ) } { x + 7 }$ 
B)  $f ( x ) = \frac { x ( x + 7 ) } { x + 6 }$ 
C)  $f ( x ) = \frac { x + 7 } { x ( x + 6 ) }$ 
D)  $f ( x ) = \frac { x + 6 } { x ( x + 7 ) }$

Question 6

Give the equations of any vertical asymptotes.
-$$h ( x ) = \frac { 5 } { x - 1 }$$

Accepted Answer

A)  $y = 1$ 
B)  $x = - 1$ 
C)  none 
D)  $x = 1$ 
A)  $y = 1$ 
B)  $x = - 1$ 
C)  none 
D)  $x = 1$

Question 7

Identify the vertex of the parabola.
-$$y = 2 x ^ { 2 } - 16 x + 33$$

Accepted Answer

A)  $( - 4 , - 1 )$ 
B)  $( - 1 , - 4 )$ 
C)  $( 4,1 )$ 
D)  $( 1,4 )$ 
A)  $( - 4 , - 1 )$ 
B)  $( - 1 , - 4 )$ 
C)  $( 4,1 )$ 
D)  $( 1,4 )$

Question 8

Find an equation for the rational function graph.
-

Accepted Answer

A)  $f ( x ) = \frac { ( x + 4 ) ^ { 2 } } { ( x - 4 ) ( x + 4 ) }$ 
B)  $f ( x ) = \frac { ( x - 4 ) ^ { 2 } } { ( x + 4 ) ( x - 4 ) }$ 
C)  $f ( x ) = \frac { ( x - 4 ) ( x + 4 ) } { ( x + 4 ) ^ { 2 } }$ 
D)  $f ( x ) = \frac { x + 4 } { x - 4 }$ 
A)  $f ( x ) = \frac { ( x + 4 ) ^ { 2 } } { ( x - 4 ) ( x + 4 ) }$ 
B)  $f ( x ) = \frac { ( x - 4 ) ^ { 2 } } { ( x + 4 ) ( x - 4 ) }$ 
C)  $f ( x ) = \frac { ( x - 4 ) ( x + 4 ) } { ( x + 4 ) ^ { 2 } }$ 
D)  $f ( x ) = \frac { x + 4 } { x - 4 }$

Question 9

Give all possible rational zeros for the following polynomial.
-$$P ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 7 x - 24$$

Accepted Answer

A)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 24$ 
B)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 8 , \pm 12 , \pm 24$ 
C)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 8 , \pm 12 , \pm 24$ 
D)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 12 , \pm 24$ 
A)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 24$ 
B)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 8 , \pm 12 , \pm 24$ 
C)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 8 , \pm 12 , \pm 24$ 
D)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 12 , \pm 24$

Question 10

Find a polynomial of least degree with only real coefficients and having the given zeros.
-$- \sqrt { 2 } , \sqrt { 2 }$, and $- 6 \mathrm { i }$

Accepted Answer

A)  $f ( x ) = x ^ { 4 } - 34 x ^ { 2 } - 72$ 
B)  $f ( x ) = x ^ { 4 } + 34 x ^ { 2 } - 72$ 
C)  $f ( x ) = x ^ { 4 } + 68 x ^ { 2 } + 72$ 
D)  $f ( x ) = x ^ { 4 } - 68 x ^ { 2 } + 72$ 
A)  $f ( x ) = x ^ { 4 } - 34 x ^ { 2 } - 72$ 
B)  $f ( x ) = x ^ { 4 } + 34 x ^ { 2 } - 72$ 
C)  $f ( x ) = x ^ { 4 } + 68 x ^ { 2 } + 72$ 
D)  $f ( x ) = x ^ { 4 } - 68 x ^ { 2 } + 72$

Question 11

Solve the problem. Round your answer to two decimal places.
-The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 4 cm on a side is 128 g, find the weight of the liquid in a cubical container 5 cm on a side.

Accepted Answer

A)  250 g 
B)  105 g 
C) 10g 
D)  125 g 
A)  250 g 
B)  105 g 
C) 10g 
D)  125 g

Question 12

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

Accepted Answer

A)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } - 4 x ^ { 2 } - 2 x + 1 \right)$ 
B)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 4 x ^ { 2 } + 6 x + 9 \right)$ 
C)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 1 \right)$ 
D)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 6 x ^ { 2 } - 4 x - 1 \right)$ 
A)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } - 4 x ^ { 2 } - 2 x + 1 \right)$ 
B)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 4 x ^ { 2 } + 6 x + 9 \right)$ 
C)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 1 \right)$ 
D)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 6 x ^ { 2 } - 4 x - 1 \right)$

Question 13

Determine which of the rational functions given below has the following feature(s).
-x-intercepts: 4 and $1 , y$-intercepts: none, vertical asymptotes: $x = 0$ and $x = - 2$, horizontal asymptote: $\mathrm { y } = 1$

Accepted Answer

A)  $f ( x ) = \frac { ( x + 4 ) ( x + 1 ) } { x ( x - 2 ) }$ 
B)  $f ( x ) = \frac { ( x - 4 ) ( x - 1 ) } { ( x + 2 ) ^ { 2 } }$ 
C)  $f ( x ) = \frac { ( x - 4 ) ( x - 1 ) } { x ( x + 2 ) }$ 
D)  $f ( x ) = \frac { ( x + 4 ) ( x + 1 ) } { ( x - 2 ) }$ 
A)  $f ( x ) = \frac { ( x + 4 ) ( x + 1 ) } { x ( x - 2 ) }$ 
B)  $f ( x ) = \frac { ( x - 4 ) ( x - 1 ) } { ( x + 2 ) ^ { 2 } }$ 
C)  $f ( x ) = \frac { ( x - 4 ) ( x - 1 ) } { x ( x + 2 ) }$ 
D)  $f ( x ) = \frac { ( x + 4 ) ( x + 1 ) } { ( x - 2 ) }$

Question 14

Use synthetic division to perform the division.
-$$\frac { x ^ { 4 } + 81 } { x - 3 }$$

Accepted Answer

A)  $x ^ { 3 } + 3 x ^ { 2 } + 9 x + 27$ 
B)  $x ^ { 3 } - 3 x ^ { 2 } + 9 x - 27 + \frac { 162 } { x - 3 }$ 
C)  $x ^ { 3 } + 3 x ^ { 2 } + 9 x + 27 + \frac { 162 } { x - 3 }$ 
D)  $x ^ { 3 } + 3 x ^ { 2 } + 9 x + 27 + \frac { 81 } { x - 3 }$ 
A)  $x ^ { 3 } + 3 x ^ { 2 } + 9 x + 27$ 
B)  $x ^ { 3 } - 3 x ^ { 2 } + 9 x - 27 + \frac { 162 } { x - 3 }$ 
C)  $x ^ { 3 } + 3 x ^ { 2 } + 9 x + 27 + \frac { 162 } { x - 3 }$ 
D)  $x ^ { 3 } + 3 x ^ { 2 } + 9 x + 27 + \frac { 81 } { x - 3 }$

Question 15

Provide an appropriate response.
-What is the smallest possible degree of the function for which this graph represents?

Accepted Answer

A)  2 
B)  5 
C)  3 
D)  4 
A)  2 
B)  5 
C)  3 
D)  4

Question 16

For the polynomial, one zero is given. Find all others.
-$$P ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 12 x + 14 ; 1 + i$$

Accepted Answer

A)  $1 - i , 7$ 
B)  $1 - i , 7 i$ 
C)  $- 7,7$ 
D)  $1 - i , - 7$ 
A)  $1 - i , 7$ 
B)  $1 - i , 7 i$ 
C)  $- 7,7$ 
D)  $1 - i , - 7$

Question 17

Solve the problem. Round your answer to two decimal places.
-The area of a circle varies directly as the square of the radius of the circle. If a circle with a radius of 5 inches has an area of $78.5$ square inches, what is the area of a circle with a radius of 14 inches?

Accepted Answer

A)  $43.96 \mathrm { in } ^ { 2 }$ 
B)  $615.44 \mathrm { in } ^ { 2 }$ 
C)  $617.84 \mathrm { in } ^ { 2 }$ 
D)  $87.92 \mathrm { in } ^ { 2 }$ 
A)  $43.96 \mathrm { in } ^ { 2 }$ 
B)  $615.44 \mathrm { in } ^ { 2 }$ 
C)  $617.84 \mathrm { in } ^ { 2 }$ 
D)  $87.92 \mathrm { in } ^ { 2 }$

Question 18

Use Descartesʹ Rule of Signs to determine the possible number of positive real zeros and the possible negative real zeros for the function.
-$$2 x ^ { 5 } - 2 x ^ { 4 } + 6 x ^ { 3 } - 3 = 0$$

Accepted Answer

A)  Positive (1), negative $( 3,1 )$ 
B)  Positive $( 4,2,0 )$, negative ( $0 )$ 
C)  Positive $( 3,1 )$, negative $( 3,1 )$ 
D)  Positive $( 3,1 )$, negative $( 0 )$ 
A)  Positive (1), negative $( 3,1 )$ 
B)  Positive $( 4,2,0 )$, negative ( $0 )$ 
C)  Positive $( 3,1 )$, negative $( 3,1 )$ 
D)  Positive $( 3,1 )$, negative $( 0 )$

Question 19

Give all possible rational zeros for the following polynomial.
-$$\mathrm { P } ( \mathrm { x } ) = 3 \mathrm { x } ^ { 3 } + 38 \mathrm { x } ^ { 2 } + 38 \mathrm { x } + 27$$

Accepted Answer

A)  $\pm 1 , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 9 } , \pm \frac { 1 } { 27 } , \pm 3$ 
B)  $\pm 1 , \pm 3 , \pm 9 , \pm 27$ 
C)  $\pm 1 , \pm 3 , \pm 6 , \pm 9 , \pm 27$ 
D)  $\pm 1 , \pm \frac { 1 } { 3 } , \pm 3 , \pm 9 , \pm 27$ 
A)  $\pm 1 , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 9 } , \pm \frac { 1 } { 27 } , \pm 3$ 
B)  $\pm 1 , \pm 3 , \pm 9 , \pm 27$ 
C)  $\pm 1 , \pm 3 , \pm 6 , \pm 9 , \pm 27$ 
D)  $\pm 1 , \pm \frac { 1 } { 3 } , \pm 3 , \pm 9 , \pm 27$

Question 20

Sketch the graph of the rational function.
-$$f ( x ) = \frac { x + 2 } { x ^ { 2 } - 9 }$$

Accepted Answer

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

Give the equatiosn of any horizontal asymptotes. - $g ( x ) = \frac { x + 5 } { x ^ { 2 } - 6 }$

Provide an appropriate response. -For what value of $c$ does the quadratic function $f ( x ) = 3 x ^ { 2 } + 8 x + c$ have exactly one $x$ -intercept?

Factor f(x) into linear factors given that k is a zero of f(x). - $f ( x ) = 8 x ^ { 3 } + 34 x ^ { 2 } + 27 x - 9 ; k = \frac { 1 } { 4 }$

Answer the question -How can the graph of $f ( x ) = \frac { 1 } { ( x - 5 ) ^ { 2 } } + 6$ be obtained from the graph of $y = \frac { 1 } { x ^ { 2 } } ?$

Find an equation for the rational function graph. -

Give the equations of any vertical asymptotes. - $h ( x ) = \frac { 5 } { x - 1 }$

Identify the vertex of the parabola. - $y = 2 x ^ { 2 } - 16 x + 33$

Find an equation for the rational function graph. -

Give all possible rational zeros for the following polynomial. - $P ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 7 x - 24$

Find a polynomial of least degree with only real coefficients and having the given zeros. - $- \sqrt { 2 } , \sqrt { 2 }$ , and $- 6 \mathrm { i }$

Solve the problem. Round your answer to two decimal places. -The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 4 cm on a side is 128 g, find the weight of the liquid in a cubical container 5 cm on a side.

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

Determine which of the rational functions given below has the following feature(s). -x-intercepts: 4 and $1 , y$ -intercepts: none, vertical asymptotes: $x = 0$ and $x = - 2$ , horizontal asymptote: $\mathrm { y } = 1$

Use synthetic division to perform the division. - $\frac { x ^ { 4 } + 81 } { x - 3 }$

Provide an appropriate response. -What is the smallest possible degree of the function for which this graph represents?

For the polynomial, one zero is given. Find all others. - $P ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 12 x + 14 ; 1 + i$

Solve the problem. Round your answer to two decimal places. -The area of a circle varies directly as the square of the radius of the circle. If a circle with a radius of 5 inches has an area of $78.5$ square inches, what is the area of a circle with a radius of 14 inches?

Use Descartesʹ Rule of Signs to determine the possible number of positive real zeros and the possible negative real zeros for the function. - $2 x ^ { 5 } - 2 x ^ { 4 } + 6 x ^ { 3 } - 3 = 0$

Give all possible rational zeros for the following polynomial. - $\mathrm { P } ( \mathrm { x } ) = 3 \mathrm { x } ^ { 3 } + 38 \mathrm { x } ^ { 2 } + 38 \mathrm { x } + 27$

Sketch the graph of the rational function. - $f ( x ) = \frac { x + 2 } { x ^ { 2 } - 9 }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x + 2 } { x ^ { 2 } - 9 }$

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

Filters

Exam 3: Polynomial and Rational Functions

Give the equatiosn of any horizontal asymptotes. - g(x)=x+5x2−6g ( x ) = \frac { x + 5 } { x ^ { 2 } - 6 }g(x)=x2−6x+5​

Provide an appropriate response. -For what value of ccc does the quadratic function f(x)=3x2+8x+cf ( x ) = 3 x ^ { 2 } + 8 x + cf(x)=3x2+8x+c have exactly one xxx -intercept?

Factor f(x) into linear factors given that k is a zero of f(x). - f(x)=8x3+34x2+27x−9;k=14f ( x ) = 8 x ^ { 3 } + 34 x ^ { 2 } + 27 x - 9 ; k = \frac { 1 } { 4 }f(x)=8x3+34x2+27x−9;k=41​

Answer the question -How can the graph of f(x)=1(x−5)2+6f ( x ) = \frac { 1 } { ( x - 5 ) ^ { 2 } } + 6f(x)=(x−5)21​+6 be obtained from the graph of y=1x2?y = \frac { 1 } { x ^ { 2 } } ?y=x21​?

Find an equation for the rational function graph. -

Give the equations of any vertical asymptotes. - h(x)=5x−1h ( x ) = \frac { 5 } { x - 1 }h(x)=x−15​

Identify the vertex of the parabola. - y=2x2−16x+33y = 2 x ^ { 2 } - 16 x + 33y=2x2−16x+33

Find an equation for the rational function graph. -

Give all possible rational zeros for the following polynomial. - P(x)=x3−9x2+7x−24P ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 7 x - 24P(x)=x3−9x2+7x−24

Find a polynomial of least degree with only real coefficients and having the given zeros. - −2,2- \sqrt { 2 } , \sqrt { 2 }−2​,2​ , and −6i- 6 \mathrm { i }−6i

Solve the problem. Round your answer to two decimal places. -The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 4 cm on a side is 128 g, find the weight of the liquid in a cubical container 5 cm on a side.

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - f(x)=−5x4+x3+2x2+3x−1;k=1f ( x ) = - 5 x ^ { 4 } + x ^ { 3 } + 2 x ^ { 2 } + 3 x - 1 ; k = 1f(x)=−5x4+x3+2x2+3x−1;k=1

Determine which of the rational functions given below has the following feature(s). -x-intercepts: 4 and 1,y1 , y1,y -intercepts: none, vertical asymptotes: x=0x = 0x=0 and x=−2x = - 2x=−2 , horizontal asymptote: y=1\mathrm { y } = 1y=1

Use synthetic division to perform the division. - x4+81x−3\frac { x ^ { 4 } + 81 } { x - 3 }x−3x4+81​

Provide an appropriate response. -What is the smallest possible degree of the function for which this graph represents?

For the polynomial, one zero is given. Find all others. - P(x)=x3+5x2−12x+14;1+iP ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 12 x + 14 ; 1 + iP(x)=x3+5x2−12x+14;1+i

Solve the problem. Round your answer to two decimal places. -The area of a circle varies directly as the square of the radius of the circle. If a circle with a radius of 5 inches has an area of 78.578.578.5 square inches, what is the area of a circle with a radius of 14 inches?

Use Descartesʹ Rule of Signs to determine the possible number of positive real zeros and the possible negative real zeros for the function. - 2x5−2x4+6x3−3=02 x ^ { 5 } - 2 x ^ { 4 } + 6 x ^ { 3 } - 3 = 02x5−2x4+6x3−3=0

Give all possible rational zeros for the following polynomial. - P(x)=3x3+38x2+38x+27\mathrm { P } ( \mathrm { x } ) = 3 \mathrm { x } ^ { 3 } + 38 \mathrm { x } ^ { 2 } + 38 \mathrm { x } + 27P(x)=3x3+38x2+38x+27

Sketch the graph of the rational function. - f(x)=x+2x2−9f ( x ) = \frac { x + 2 } { x ^ { 2 } - 9 }f(x)=x2−9x+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

Filters

Give the equatiosn of any horizontal asymptotes. - $g ( x ) = \frac { x + 5 } { x ^ { 2 } - 6 }$

Provide an appropriate response. -For what value of $c$ does the quadratic function $f ( x ) = 3 x ^ { 2 } + 8 x + c$ have exactly one $x$ -intercept?

Factor f(x) into linear factors given that k is a zero of f(x). - $f ( x ) = 8 x ^ { 3 } + 34 x ^ { 2 } + 27 x - 9 ; k = \frac { 1 } { 4 }$

Answer the question -How can the graph of $f ( x ) = \frac { 1 } { ( x - 5 ) ^ { 2 } } + 6$ be obtained from the graph of $y = \frac { 1 } { x ^ { 2 } } ?$

Give the equations of any vertical asymptotes. - $h ( x ) = \frac { 5 } { x - 1 }$

Identify the vertex of the parabola. - $y = 2 x ^ { 2 } - 16 x + 33$

Give all possible rational zeros for the following polynomial. - $P ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 7 x - 24$

Find a polynomial of least degree with only real coefficients and having the given zeros. - $- \sqrt { 2 } , \sqrt { 2 }$ , and $- 6 \mathrm { i }$

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

Determine which of the rational functions given below has the following feature(s). -x-intercepts: 4 and $1 , y$ -intercepts: none, vertical asymptotes: $x = 0$ and $x = - 2$ , horizontal asymptote: $\mathrm { y } = 1$

Use synthetic division to perform the division. - $\frac { x ^ { 4 } + 81 } { x - 3 }$

For the polynomial, one zero is given. Find all others. - $P ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 12 x + 14 ; 1 + i$

Solve the problem. Round your answer to two decimal places. -The area of a circle varies directly as the square of the radius of the circle. If a circle with a radius of 5 inches has an area of $78.5$ square inches, what is the area of a circle with a radius of 14 inches?

Use Descartesʹ Rule of Signs to determine the possible number of positive real zeros and the possible negative real zeros for the function. - $2 x ^ { 5 } - 2 x ^ { 4 } + 6 x ^ { 3 } - 3 = 0$

Give all possible rational zeros for the following polynomial. - $\mathrm { P } ( \mathrm { x } ) = 3 \mathrm { x } ^ { 3 } + 38 \mathrm { x } ^ { 2 } + 38 \mathrm { x } + 27$

Sketch the graph of the rational function. - $f ( x ) = \frac { x + 2 } { x ^ { 2 } - 9 }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x + 2 } { x ^ { 2 } - 9 }$