Question 1

Find a cubic polynomial with real coefficients having roots x = -2 and x = 1 + 4i. Assume a lead coefficient of 1.

Accepted Answer

A)  P(x) = x3 + 13x + 34 
B)  P(x) = x3 + 13x - 34 
C)  P(x) = x3 + 4x2 + 21x + 34 
D)  P(x) = x3 - 4x2 + 21x - 34 
A)  P(x) = x3 + 13x + 34 
B)  P(x) = x3 + 13x - 34 
C)  P(x) = x3 + 4x2 + 21x + 34 
D)  P(x) = x3 - 4x2 + 21x - 34

Question 2

Use the following to answer questions :   (Gridlines are spaced one unit apart.)
-Use the direction/approach notation to describe the end behavior of the graph. (This should produce four statements.)

Accepted Answer

as x → ∞, y → 2⁺, as

Question 3

Use the remainder theorem to show x = 2i is a zero of P(x) = x3 + 2x2 + 4x + 8.

Accepted Answer

Question 4

Use synthetic division and the remainder theorem to evaluate P(-3) if P(x) = 2x3 - 3x2 + 5x - 13.

Accepted Answer

A)  -110 
B)  -109 
C)  -108 
D)  -107 
A)  -110 
B)  -109 
C)  -108 
D)  -107

Question 5

Give the location of the vertical asymptote(s) if they exist, and state the function's domain in set notation.

Accepted Answer

A)  x = 2; {x | x $\in$ R, x ? 2} 
B)  x =   ; {x | x $\in$ R, x ?
  } 
C)  x = -5, x = -1; {x | x $\in$ R, x ? -5, x ? -1} 
D)  No vertical asymptote; {x | x $\in$ R} 
A)  x = 2; {x | x $\in$ R, x ? 2} 
B)  x =   ; {x | x $\in$ R, x ?
  } 
C)  x = -5, x = -1; {x | x $\in$ R, x ? -5, x ? -1} 
D)  No vertical asymptote; {x | x $\in$ R}

Question 6

Solve the inequality using a number line and the behavior of the graph at each zero. Write your answer in interval notation.

Accepted Answer

A)  x $\in$  (-?, -3] $\cup$  [1, 3] $\cup$  (11, ?) 
B)  x $\in$  (-?, -3] $\cup$  (1, 3] $\cup$  (11, ?) 
C)  x $\in$  [-3, 1) $\cup$  [3, 11) 
D)  x $\in$  (-3, 1] $\cup$  (3, 11] 
A)  x $\in$  (-?, -3] $\cup$  [1, 3] $\cup$  (11, ?) 
B)  x $\in$  (-?, -3] $\cup$  (1, 3] $\cup$  (11, ?) 
C)  x $\in$  [-3, 1) $\cup$  [3, 11) 
D)  x $\in$  (-3, 1] $\cup$  (3, 11]

Question 7

State the degree, end behavior, and y-intercept of the function.
f(x) = -(x - 5)(x - 1)8(x - 2)2

Accepted Answer

degree 11,

Question 8

Graph the function using end behavior, intercepts and by completing the square to write the function in shifted form. Clearly state the transformations used to obtain the graph, and label the vertex and all intercepts (if they exist). Use the quadratic formula to find the x-intercepts. f(x) = 3x2 + 5x + 1

Accepted Answer

A)  left 1, down 2, stretched vertically
  
B)  right 1, down 2, stretched vertically
  
C)  left .8, down 1.1, stretched vertically
  
D)  right .8, down 1.1, stretched vertically
  
A)  left 1, down 2, stretched vertically
  
B)  right 1, down 2, stretched vertically
  
C)  left .8, down 1.1, stretched vertically
  
D)  right .8, down 1.1, stretched vertically

Question 9

Find all zeroes (real and complex) of the polynomial.
p(x) = 6x3 + 29x2 - 149x + 24

Accepted Answer

Question 10

The electrical resistance of a copper wire varies directly with its length and inversely with the square of the diameter of the wire. If a wire 20 m long with a diameter of 4 mm has a resistance of 35   , find the resistance of a wire 30 mm long with a diameter of 4.5 mm. Round your answer to two decimal places.

Accepted Answer

A)  39.64   
B)  40.26   
C)  41.48   
D)  42.35   
A)  39.64   
B)  40.26   
C)  41.48   
D)  42.35

Question 11

Graph the function using end behavior, intercepts and by completing the square to write the function in shifted form. Clearly state the transformations used to obtain the graph, and label the vertex and all intercepts (if they exist). Use the quadratic formula to find the x-intercepts.
f(x) = -x2 + 4x - 3

Accepted Answer

right 2, u

Question 12

Use the following to answer questions :
y varies directly with x;
y = 8.4 when x = 24.
-The amount of money Molly's parents give her for reading varies directly with the number of pages she reads. Molly receives $2.50 for reading 125 pages.
(a) What is the constant of variation?
(b) Write the variation equation.
(c) How much will Molly receive for reading 150 pages?

Accepted Answer

(a) 0.02
(

Question 13

Graph the function using the Guidelines for Graphing Rational Functions, which is simply modified to include nonlinear asymptotes. Clearly state all intercepts and asymptotes and any additional points used to sketch the graph.

Accepted Answer

Vertical asymptote: x = -2; Ob

Question 14

Determine the equation of the function shown.

Accepted Answer

A)  f(x) = -x2 + 1 
B)  f(x) = -x2 - 1 
C)  f(x) = -(x + 1)2 
D)  f(x) = -(x - 1)2 
A)  f(x) = -x2 + 1 
B)  f(x) = -x2 - 1 
C)  f(x) = -(x + 1)2 
D)  f(x) = -(x - 1)2

Question 15

Graph the function. If there is a removable discontinuity, repair the break by redefining the function using an appropriate piecewise-defined function.

Accepted Answer

@#IMG-DLM& @#IMG-DLM& (Gridlin

Question 16

Find a cubic polynomial with real coefficients having roots x = -3 and x = -i. Assume a lead coefficient of 1.

Accepted Answer

P(x) = x³ +

Question 17

Use the following to answer questions :
A varies directly with B and inversely with C squared, and A = 93.75 when B = 20 and C = 1.2.
-Write the variation equation.

Accepted Answer

The answer of Use the following to answer questions :
A...

Question 18

Solve the inequality using a number line and the behavior of the graph at each zero. Write your answer in interval notation.

Accepted Answer

A)  x  $\in$  (-?, -10) $\cup$  (-4, ?) 
B)  x  $\in$  (-?, -4) 
C)  x  $\in$  (-4, ?) 
D)  x  $\in$  (-?, ?) 
A)  x  $\in$  (-?, -10) $\cup$  (-4, ?) 
B)  x  $\in$  (-?, -4) 
C)  x  $\in$  (-4, ?) 
D)  x  $\in$  (-?, ?)

Question 19

Use synthetic division and the remainder theorem to evaluate P(4) if P(x) = x3 - 5x2 - 4x + 20. Verify using a second method.

Accepted Answer

@#IMG-DLM& Since the remainder

Question 20

Graph the function using end behavior, intercepts and by completing the square to write the function in shifted form. Clearly state the transformations used to obtain the graph, and label the vertex and all intercepts (if they exist). Use the quadratic formula to find the x-intercepts.
f(x) = 2x2 + 9x + 4

Accepted Answer

left 9/4,

Find a cubic polynomial with real coefficients having roots x = -2 and x = 1 + 4i. Assume a lead coefficient of 1.

Use the following to answer questions : (Gridlines are spaced one unit apart.) -Use the direction/approach notation to describe the end behavior of the graph. (This should produce four statements.)

Use the remainder theorem to show x = 2i is a zero of P(x) = x³ + 2x² + 4x + 8.

Use synthetic division and the remainder theorem to evaluate P(-3) if P(x) = 2x³ - 3x² + 5x - 13.

Give the location of the vertical asymptote(s) if they exist, and state the function's domain in set notation.

Solve the inequality using a number line and the behavior of the graph at each zero. Write your answer in interval notation.

State the degree, end behavior, and y-intercept of the function. f(x) = -(x - 5)(x - 1)⁸(x - 2)²

Find all zeroes (real and complex) of the polynomial. p(x) = 6x³ + 29x² - 149x + 24

Graph the function using the Guidelines for Graphing Rational Functions, which is simply modified to include nonlinear asymptotes. Clearly state all intercepts and asymptotes and any additional points used to sketch the graph.

Determine the equation of the function shown.

Graph the function. If there is a removable discontinuity, repair the break by redefining the function using an appropriate piecewise-defined function.

Find a cubic polynomial with real coefficients having roots x = -3 and x = -i. Assume a lead coefficient of 1.

Use the following to answer questions : A varies directly with B and inversely with C squared, and A = 93.75 when B = 20 and C = 1.2. -Write the variation equation.

Solve the inequality using a number line and the behavior of the graph at each zero. Write your answer in interval notation.

Use synthetic division and the remainder theorem to evaluate P(4) if P(x) = x³ - 5x² - 4x + 20. Verify using a second method.

Equations and Inequalities

Relations, Functions and Graphs

Exponential and Logarithmic Functions

Introduction to Trigonometric Functions

Trigonometric Identities, Inverses, and Equations

Applications of Trigonometry

Systems of Equations and Inequalities

Analytical Geometry

Additional Topics in Algebra

Bridges to Calculus - an Introduction to Limits

Review of Basic Concepts and Skills

Filters

Exam 3: Polynomial and Rational Functions

Find a cubic polynomial with real coefficients having roots x = -2 and x = 1 + 4i. Assume a lead coefficient of 1.

Use the following to answer questions : (Gridlines are spaced one unit apart.) -Use the direction/approach notation to describe the end behavior of the graph. (This should produce four statements.)

Use the remainder theorem to show x = 2i is a zero of P(x) = x3 + 2x2 + 4x + 8.

Use synthetic division and the remainder theorem to evaluate P(-3) if P(x) = 2x3 - 3x2 + 5x - 13.

Give the location of the vertical asymptote(s) if they exist, and state the function's domain in set notation.

Solve the inequality using a number line and the behavior of the graph at each zero. Write your answer in interval notation.

State the degree, end behavior, and y-intercept of the function. f(x) = -(x - 5)(x - 1)8(x - 2)2

Find all zeroes (real and complex) of the polynomial. p(x) = 6x3 + 29x2 - 149x + 24

Graph the function using the Guidelines for Graphing Rational Functions, which is simply modified to include nonlinear asymptotes. Clearly state all intercepts and asymptotes and any additional points used to sketch the graph.

Determine the equation of the function shown.

Graph the function. If there is a removable discontinuity, repair the break by redefining the function using an appropriate piecewise-defined function.

Find a cubic polynomial with real coefficients having roots x = -3 and x = -i. Assume a lead coefficient of 1.

Use the following to answer questions : A varies directly with B and inversely with C squared, and A = 93.75 when B = 20 and C = 1.2. -Write the variation equation.

Solve the inequality using a number line and the behavior of the graph at each zero. Write your answer in interval notation.

Use synthetic division and the remainder theorem to evaluate P(4) if P(x) = x3 - 5x2 - 4x + 20. Verify using a second method.

Equations and Inequalities

Relations, Functions and Graphs

Exponential and Logarithmic Functions

Introduction to Trigonometric Functions

Trigonometric Identities, Inverses, and Equations

Applications of Trigonometry

Systems of Equations and Inequalities

Analytical Geometry

Additional Topics in Algebra

Bridges to Calculus - an Introduction to Limits

Review of Basic Concepts and Skills

Filters

Use the remainder theorem to show x = 2i is a zero of P(x) = x³ + 2x² + 4x + 8.

Use synthetic division and the remainder theorem to evaluate P(-3) if P(x) = 2x³ - 3x² + 5x - 13.

State the degree, end behavior, and y-intercept of the function. f(x) = -(x - 5)(x - 1)⁸(x - 2)²

Find all zeroes (real and complex) of the polynomial. p(x) = 6x³ + 29x² - 149x + 24

Use synthetic division and the remainder theorem to evaluate P(4) if P(x) = x³ - 5x² - 4x + 20. Verify using a second method.