Question 1

Find the vertex.
f(x) = x2 + 10x - 8

Accepted Answer

Question 2

Determine the location of the horizontal asymptote if it exists. Then determine whether the graph will cross the asymptote, and if so, where it crosses.

Accepted Answer

y = 2; cro

Question 3

Find the intercepts. Round to the nearest tenth if necessary.
f(x) = 3x2 + 8x - 6

Accepted Answer

(-3.3, 0),

Question 4

Use the following to answer questions :   (Gridlines are spaced one unit apart.)
-State the equations of the horizontal and vertical asymptotes.

Accepted Answer

A)  y = -4, x = 2 
B)  y = 4, x = -2 
C)  y = 2, x = -4 
D)  y = -2, x = 4 
A)  y = -4, x = 2 
B)  y = 4, x = -2 
C)  y = 2, x = -4 
D)  y = -2, x = 4

Question 5

Use synthetic division and the remainder theorem to show that x = -2 is a zero of P(x) = x3 - 4x2 - 4x + 16.

Accepted Answer

@#IMG-DLM& Since the remainder

Question 6

Use the vertex/intercept formula,   , to find zeroes, real or complex of the formula. f(x) = 3(x + 1)2 - 2

Accepted Answer

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

Question 7

Use the following to answer questions :   (Gridlines are spaced one unit apart.)
-Use the graph to estimate the zeroes of the function, then state whether their multiplicity is even or odd.

Accepted Answer

A)  -1, even; 2 odd 
B)  -1, odd; 2 even 
C)  -1, even; 2 even 
D)  -1, odd; 2 odd 
A)  -1, even; 2 odd 
B)  -1, odd; 2 even 
C)  -1, even; 2 even 
D)  -1, odd; 2 odd

Question 8

Find the intercepts.
f(x) = x2 - 10x + 24

Accepted Answer

(6, 0), (4

Question 9

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: none; Nonl

Question 10

Sketch the graph of the function using the degree, end behavior, x- and y-intercepts, zeroes of multiplicity, and a few midinterval points to round out the graph. Connect all points with a smooth, continuous curve.
f(x) = (x - 1)3(x + 2)(x + 3)

Accepted Answer

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 = 4, no 
B)  x = 4, yes 
C)  x = -1, no; x = 2, no 
D)  x = -1, yes; x = 2, yes 
A)  x = 4, no 
B)  x = 4, yes 
C)  x = -1, no; x = 2, no 
D)  x = -1, yes; x = 2, yes

Question 12

Use the rational roots theorem to write the function in factored form and find all zeroes. Note a = 1. p(x) = x4 + 6x3 - 13x2 - 66x + 72

Accepted Answer

A)  p(x) = (x - 1)(x - 3)(x + 4)(x + 6); zeroes: 1, 3, -4, -6 
B)  p(x) = (x + 1)(x + 3)(x - 4)(x - 6); zeroes: -1, -3, 4, 6 
C)  p(x) = (x - 1)(x + 3)(x - 4)(x + 6); zeroes: 1, -3, 4, -6 
D)  p(x) = (x + 1)(x - 3)(x + 4)(x - 6); zeroes: -1, 3, -4, 6 
A)  p(x) = (x - 1)(x - 3)(x + 4)(x + 6); zeroes: 1, 3, -4, -6 
B)  p(x) = (x + 1)(x + 3)(x - 4)(x - 6); zeroes: -1, -3, 4, 6 
C)  p(x) = (x - 1)(x + 3)(x - 4)(x + 6); zeroes: 1, -3, 4, -6 
D)  p(x) = (x + 1)(x - 3)(x + 4)(x - 6); zeroes: -1, 3, -4, 6

Question 13

Determine the location of the horizontal asymptote if it exists. Then determine whether the graph will cross the asymptote, and if so, where it crosses.

Accepted Answer

A)  y = 0; crosses at (1, 0) 
B)  y = 0; does not cross 
C)  y = 2; does not cross 
D)  No horizontal asymptote 
A)  y = 0; crosses at (1, 0) 
B)  y = 0; does not cross 
C)  y = 2; does not cross 
D)  No horizontal asymptote

Question 14

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

Accepted Answer

The answer of Solve the inequality using a number line...

Question 15

Gather information on the polynomial using the rational roots theorem, testing for 1 and -1, Descartes's rule of signs, and the upper and lower bounds property. Respond explicitly to each.
p(x) = x4 - 3x3 + 9x - 27

Accepted Answer

Possible rational roots: {±1,

Question 16

State the end behavior and y-intercept of the function. Do not graph.
f(x) = x5 + 5x4 - 5x2 - 3x + 5

Accepted Answer

Question 17

Use the following to answer questions :
y varies inversely with x; y = 12,600 when x = 0.2.
-The days required to complete a project varies inversely with the number of employees working on the project. It takes 88 days to complete the project if 5 employees work on it.
(a) What is the constant of variation?
(b) Write the variation equation.
(c) How long will it take to complete the project if 22 employees work on it?

Accepted Answer

(a) 440
(b

Question 18

Use the Guidelines for Graphing Rational Functions to graph   .

Accepted Answer

@#IMG-DLM& (Gridline

Question 19

Use the following to answer questions :   (Gridlines are spaced one unit apart.)
-Give the equation related to the graph. Assume |a| = 1.

Accepted Answer

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

Question 20

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) = 4x4 - 3x3 - 30x2 - x + 30

Accepted Answer

Find the vertex. f(x) = x² + 10x - 8

Determine the location of the horizontal asymptote if it exists. Then determine whether the graph will cross the asymptote, and if so, where it crosses.

Find the intercepts. Round to the nearest tenth if necessary. f(x) = 3x² + 8x - 6

Use the following to answer questions : (Gridlines are spaced one unit apart.) -State the equations of the horizontal and vertical asymptotes.

Use synthetic division and the remainder theorem to show that x = -2 is a zero of P(x) = x³ - 4x² - 4x + 16.

Use the vertex/intercept formula, , to find zeroes, real or complex of the formula. f(x) = 3(x + 1)² - 2

Use the following to answer questions : (Gridlines are spaced one unit apart.) -Use the graph to estimate the zeroes of the function, then state whether their multiplicity is even or odd.

Find the intercepts. f(x) = x² - 10x + 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.

Sketch the graph of the function using the degree, end behavior, x- and y-intercepts, zeroes of multiplicity, and a few midinterval points to round out the graph. Connect all points with a smooth, continuous curve. f(x) = (x - 1)³(x + 2)(x + 3)

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.

Use the rational roots theorem to write the function in factored form and find all zeroes. Note a = 1. p(x) = x⁴ + 6x³ - 13x² - 66x + 72

Determine the location of the horizontal asymptote if it exists. Then determine whether the graph will cross the asymptote, and if so, where it crosses.

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

Gather information on the polynomial using the rational roots theorem, testing for 1 and -1, Descartes's rule of signs, and the upper and lower bounds property. Respond explicitly to each. p(x) = x⁴ - 3x³ + 9x - 27

State the end behavior and y-intercept of the function. Do not graph. f(x) = x⁵ + 5x⁴ - 5x²- 3x + 5

Use the Guidelines for Graphing Rational Functions to graph .

Use the following to answer questions : (Gridlines are spaced one unit apart.) -Give the equation related to the graph. Assume |a| = 1.

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) = 4x⁴ - 3x³ - 30x² - x + 30

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

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Exam 3: Polynomial and Rational Functions

Find the vertex. f(x) = x2 + 10x - 8

Determine the location of the horizontal asymptote if it exists. Then determine whether the graph will cross the asymptote, and if so, where it crosses.

Find the intercepts. Round to the nearest tenth if necessary. f(x) = 3x2 + 8x - 6

Use the following to answer questions : (Gridlines are spaced one unit apart.) -State the equations of the horizontal and vertical asymptotes.

Use synthetic division and the remainder theorem to show that x = -2 is a zero of P(x) = x3 - 4x2 - 4x + 16.

Use the vertex/intercept formula, , to find zeroes, real or complex of the formula. f(x) = 3(x + 1)2 - 2

Use the following to answer questions : (Gridlines are spaced one unit apart.) -Use the graph to estimate the zeroes of the function, then state whether their multiplicity is even or odd.

Find the intercepts. f(x) = x2 - 10x + 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.

Sketch the graph of the function using the degree, end behavior, x- and y-intercepts, zeroes of multiplicity, and a few midinterval points to round out the graph. Connect all points with a smooth, continuous curve. f(x) = (x - 1)3(x + 2)(x + 3)

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.

Use the rational roots theorem to write the function in factored form and find all zeroes. Note a = 1. p(x) = x4 + 6x3 - 13x2 - 66x + 72

Determine the location of the horizontal asymptote if it exists. Then determine whether the graph will cross the asymptote, and if so, where it crosses.

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

Gather information on the polynomial using the rational roots theorem, testing for 1 and -1, Descartes's rule of signs, and the upper and lower bounds property. Respond explicitly to each. p(x) = x4 - 3x3 + 9x - 27

State the end behavior and y-intercept of the function. Do not graph. f(x) = x5 + 5x4 - 5x2 - 3x + 5

Use the Guidelines for Graphing Rational Functions to graph .

Use the following to answer questions : (Gridlines are spaced one unit apart.) -Give the equation related to the graph. Assume |a| = 1.

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) = 4x4 - 3x3 - 30x2 - x + 30

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

Find the vertex. f(x) = x² + 10x - 8

Find the intercepts. Round to the nearest tenth if necessary. f(x) = 3x² + 8x - 6

Use synthetic division and the remainder theorem to show that x = -2 is a zero of P(x) = x³ - 4x² - 4x + 16.

Use the vertex/intercept formula, , to find zeroes, real or complex of the formula. f(x) = 3(x + 1)² - 2

Find the intercepts. f(x) = x² - 10x + 24

Sketch the graph of the function using the degree, end behavior, x- and y-intercepts, zeroes of multiplicity, and a few midinterval points to round out the graph. Connect all points with a smooth, continuous curve. f(x) = (x - 1)³(x + 2)(x + 3)

Use the rational roots theorem to write the function in factored form and find all zeroes. Note a = 1. p(x) = x⁴ + 6x³ - 13x² - 66x + 72

Gather information on the polynomial using the rational roots theorem, testing for 1 and -1, Descartes's rule of signs, and the upper and lower bounds property. Respond explicitly to each. p(x) = x⁴ - 3x³ + 9x - 27

State the end behavior and y-intercept of the function. Do not graph. f(x) = x⁵ + 5x⁴ - 5x²- 3x + 5

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) = 4x⁴ - 3x³ - 30x² - x + 30