Question 1

Use the Guidelines for Graphing Rational Functions to graph   .

Accepted Answer

(Gridlines are spaced one unit apart.)

Question 2

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

Accepted Answer

A)    
B)    
C)    
D)  No removable discontinuity 
A)    
B)    
C)    
D)  No removable discontinuity A

Question 3

List all possible rational roots for the polynomial but do not solve.
f(x) = 21x3 - 5x2 + x - 175

Accepted Answer

Question 4

Find the zeroes of the polynomial using any combination of the rational roots theorem, synthetic division, testing for 1 and -1, and/or the remainder and factor theorems. p(x) = x4 + 3x3 + 3x2 - 17x - 18

Accepted Answer

A)  -1, 2,   
B)  1, -2,   
C)  -1, 2,   
D)  1, -2,   
A)  -1, 2,   
B)  1, -2,   
C)  -1, 2,   
D)  1, -2,

Question 5

A polynomial P of degree 3 with integer coefficients has zeroes x = 3, x = -9, and x = 1. Use the factor theorem to write the polynomial in factored form.

Accepted Answer

A)  P(x) = (x + 3)(x - 9)(x + 1) 
B)  P(x) = (x - 3)(x + 9)(x - 1) 
C)  P(x) = (3x + 1)(-9x + 1)(x + 1) 
D)  P(x) = (-3x + 1)(9x + 1)(-x + 1) 
A)  P(x) = (x + 3)(x - 9)(x + 1) 
B)  P(x) = (x - 3)(x + 9)(x - 1) 
C)  P(x) = (3x + 1)(-9x + 1)(x + 1) 
D)  P(x) = (-3x + 1)(9x + 1)(-x + 1)

Question 6

Use the following to answer questions :
y varies directly with x;
y = 8.4 when x = 24.
-Find the constant of variation.

Accepted Answer

A)  0.065 
B)  0.65 
C)  1.65 
D)  6.5 
A)  0.065 
B)  0.65 
C)  1.65 
D)  6.5

Question 7

Use the following to answer questions :   (Gridlines are spaced one unit apart.)
-State the range of the function.

Accepted Answer

A)  y $\in$ (-?, -4) $\cup$  (-4, ?) 
B)  y $\in$ (-?, 4) $\cup$  (4, ?) 
C)  y $\in$ (-?, -2) $\cup$  (-2, ?) 
D)  y $\in$ (-?, 2) $\cup$  (2, ?) 
A)  y $\in$ (-?, -4) $\cup$  (-4, ?) 
B)  y $\in$ (-?, 4) $\cup$  (4, ?) 
C)  y $\in$ (-?, -2) $\cup$  (-2, ?) 
D)  y $\in$ (-?, 2) $\cup$  (2, ?)

Question 8

Use the following to answer questions :
y varies inversely with x; y = 12,600 when x = 0.2.
-Write the variation equation.

Accepted Answer

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

Question 9

Find all zeroes (real and complex) of the polynomial.
p(x) = 4x3 - 5x2 - 23x + 6

Accepted Answer

Question 10

For the complex polynomial below, one of its zeroes is z = 5i. Use the given zero to help find all zeroes of the polynomial, then write the polynomial in completely factored form. Hint: synthetic division and the quadratic formula can be applied to all polynomials, even those with complex coefficients.
C(z) = z3 + (1 - 5i)z2 + (-6 - 5i)z + 30i.

Accepted Answer

C(z) = (z

Question 11

Give the location of the vertical asymptote(s) if they exist, and state whether function values will change sign (positive to negative or negative to positive) from one side of the asymptote to the other.

Accepted Answer

A)  x = 1, no 
B)  x = 1, yes 
C)  x = -4, no; x = 1, no 
D)  x = -4, yes; x = 1, yes 
A)  x = 1, no 
B)  x = 1, yes 
C)  x = -4, no; x = 1, no 
D)  x = -4, yes; x = 1, yes

Question 12

A polynomial P of degree 3 with integer coefficients has zeroes x = 5,   , and   . Use the factor theorem to write the polynomial in factored form and standard form.

Accepted Answer

P(x) = (x

Question 13

Solve the inequality using a number line and the behavior of the graph at each zero. Write your answer in interval notation. (x + 1)(x - 5)3(x - 4)2 ? 0

Accepted Answer

A)  x $\in$ [-1, 5] 
B)  x $\in$ (-?, -1] $\cup$  [5, ?) 
C)  x $\in$ [-1, 4] $\cup$  [5, ?) 
D)  x $\in$  (-?, -1] $\cup$  [4, ?) 
A)  x $\in$ [-1, 5] 
B)  x $\in$ (-?, -1] $\cup$  [5, ?) 
C)  x $\in$ [-1, 4] $\cup$  [5, ?) 
D)  x $\in$  (-?, -1] $\cup$  [4, ?)

Question 14

Find a polynomial P with real coefficients having degree 5, only one real, rational root, and zeroes x = 2 and x = 1 + 5i. Assume a lead coefficient of 1. Leave your answer in factored form.

Accepted Answer

P(x) = (x

Question 15

Find a quartic polynomial (degree 4) with real coefficients having roots x =   and x = 1 +   i. Assume a lead coefficient of 1.

Accepted Answer

P(x) = x⁴ -

Question 16

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

right 9/4,

Question 17

Graph the function using the concavity, y-intercept, x-intercept(s), vertex, and symmetry. f(x) =

Accepted Answer

A)   
(Gridlines are spaced one unit apart.) 
B)   
(Gridlines are spaced one unit apart.) 
C)   
(Gridlines are spaced one unit apart.) 
D)   
(Gridlines are spaced one unit apart.) 
A)   
(Gridlines are spaced one unit apart.) 
B)   
(Gridlines are spaced one unit apart.) 
C)   
(Gridlines are spaced one unit apart.) 
D)   
(Gridlines are spaced one unit apart.)

Question 18

Use the rational roots theorem to write the function in factored form and find all zeroes. Note a = 1.
p(x) = x3 + 4x2 - 9x - 36

Accepted Answer

(x - 3)(x

Question 19

Use the following to answer questions :
y varies inversely with x; y = 12,600 when x = 0.2.
-Complete the table.

Accepted Answer

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

Question 20

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

Use the Guidelines for Graphing Rational Functions to graph .

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

List all possible rational roots for the polynomial but do not solve. f(x) = 21x³ - 5x² + x - 175

Find the zeroes of the polynomial using any combination of the rational roots theorem, synthetic division, testing for 1 and -1, and/or the remainder and factor theorems. p(x) = x⁴ + 3x³ + 3x² - 17x - 18

A polynomial P of degree 3 with integer coefficients has zeroes x = 3, x = -9, and x = 1. Use the factor theorem to write the polynomial in factored form.

Use the following to answer questions : y varies directly with x; y = 8.4 when x = 24. -Find the constant of variation.

Use the following to answer questions : (Gridlines are spaced one unit apart.) -State the range of the function.

Use the following to answer questions : y varies inversely with x; y = 12,600 when x = 0.2. -Write the variation equation.

Find all zeroes (real and complex) of the polynomial. p(x) = 4x³ - 5x² - 23x + 6

Give the location of the vertical asymptote(s) if they exist, and state whether function values will change sign (positive to negative or negative to positive) from one side of the asymptote to the other.

A polynomial P of degree 3 with integer coefficients has zeroes x = 5, , and . Use the factor theorem to write the polynomial in factored form and standard form.

Solve the inequality using a number line and the behavior of the graph at each zero. Write your answer in interval notation. (x + 1)(x - 5)³(x - 4)² ? 0

Find a polynomial P with real coefficients having degree 5, only one real, rational root, and zeroes x = 2 and x = 1 + 5i. Assume a lead coefficient of 1. Leave your answer in factored form.

Find a quartic polynomial (degree 4) with real coefficients having roots x = and x = 1 + i. Assume a lead coefficient of 1.

Graph the function using the concavity, y-intercept, x-intercept(s), vertex, and symmetry. f(x) =

Use the rational roots theorem to write the function in factored form and find all zeroes. Note a = 1. p(x) = x³ + 4x² - 9x - 36

Use the following to answer questions : y varies inversely with x; y = 12,600 when x = 0.2. -Complete the table.

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

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

Use the Guidelines for Graphing Rational Functions to graph .

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

List all possible rational roots for the polynomial but do not solve. f(x) = 21x3 - 5x2 + x - 175

Find the zeroes of the polynomial using any combination of the rational roots theorem, synthetic division, testing for 1 and -1, and/or the remainder and factor theorems. p(x) = x4 + 3x3 + 3x2 - 17x - 18

A polynomial P of degree 3 with integer coefficients has zeroes x = 3, x = -9, and x = 1. Use the factor theorem to write the polynomial in factored form.

Use the following to answer questions : y varies directly with x; y = 8.4 when x = 24. -Find the constant of variation.

Use the following to answer questions : (Gridlines are spaced one unit apart.) -State the range of the function.

Use the following to answer questions : y varies inversely with x; y = 12,600 when x = 0.2. -Write the variation equation.

Find all zeroes (real and complex) of the polynomial. p(x) = 4x3 - 5x2 - 23x + 6

Give the location of the vertical asymptote(s) if they exist, and state whether function values will change sign (positive to negative or negative to positive) from one side of the asymptote to the other.

A polynomial P of degree 3 with integer coefficients has zeroes x = 5, , and . Use the factor theorem to write the polynomial in factored form and standard form.

Solve the inequality using a number line and the behavior of the graph at each zero. Write your answer in interval notation. (x + 1)(x - 5)3(x - 4)2 ? 0

Find a polynomial P with real coefficients having degree 5, only one real, rational root, and zeroes x = 2 and x = 1 + 5i. Assume a lead coefficient of 1. Leave your answer in factored form.

Find a quartic polynomial (degree 4) with real coefficients having roots x = and x = 1 + i. Assume a lead coefficient of 1.

Graph the function using the concavity, y-intercept, x-intercept(s), vertex, and symmetry. f(x) =

Use the rational roots theorem to write the function in factored form and find all zeroes. Note a = 1. p(x) = x3 + 4x2 - 9x - 36

Use the following to answer questions : y varies inversely with x; y = 12,600 when x = 0.2. -Complete the table.

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

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

List all possible rational roots for the polynomial but do not solve. f(x) = 21x³ - 5x² + x - 175

Find the zeroes of the polynomial using any combination of the rational roots theorem, synthetic division, testing for 1 and -1, and/or the remainder and factor theorems. p(x) = x⁴ + 3x³ + 3x² - 17x - 18

Find all zeroes (real and complex) of the polynomial. p(x) = 4x³ - 5x² - 23x + 6

Solve the inequality using a number line and the behavior of the graph at each zero. Write your answer in interval notation. (x + 1)(x - 5)³(x - 4)² ? 0

Use the rational roots theorem to write the function in factored form and find all zeroes. Note a = 1. p(x) = x³ + 4x² - 9x - 36