Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN: 9781305071742
Author: James Stewart, Lothar Redlin, Saleem Watson
Publisher: Cengage Learning
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Question
Chapter 3.6, Problem 20E
To determine
To Graph:
The rational function
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Check out a sample textbook solutionStudents have asked these similar questions
Use transformations of the graph of y = 1/x to graph the rational function, as in Example 2.
(x) = *+5
x + 6
y
y
2
-15
- 10
-5
10
15
-15
- 10
10
15
2
-2
y
4
2
2
wwwwww
-15
- 10
-5
10
15
-15
- 10
5
10
15
-2
-2
State the domain and range. (Enter your answers using interval notation.)
domain
range
EXAMPLE 2 Using Transformations to Graph Rational Functions
Graph each rational function, and state the domain and range.
2
3x + 5
(a) r(x)
(b) s(x)
%3D
x - 3
x + 2
Analyze the key features of the graph of f(x) shown below.
2
-7 -6 -5
-2
-4
-1
(-2, -1)
-1
-3
(-4, -3)
-4
-5
-6
-7
Use rules of transformations and the parent function to formulate an equation for the rational function
shown in the graph. Show all your work.
Chapter 3 Solutions
Algebra and Trigonometry (MindTap Course List)
Ch. 3.1 - To put the quadratic function fx=ax2+bx+c in...Ch. 3.1 - Prob. 2ECh. 3.1 - Prob. 3ECh. 3.1 - Prob. 4ECh. 3.1 - 5-8 Graphs of Quadratic Functions The graph of a...Ch. 3.1 - Prob. 6ECh. 3.1 - Prob. 7ECh. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10E
Ch. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Prob. 13ECh. 3.1 - Prob. 14ECh. 3.1 - Prob. 15ECh. 3.1 - Prob. 16ECh. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - Prob. 20ECh. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - Prob. 31ECh. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - Prob. 39ECh. 3.1 - Prob. 40ECh. 3.1 - Prob. 41ECh. 3.1 - Prob. 42ECh. 3.1 - Prob. 43ECh. 3.1 - Prob. 44ECh. 3.1 - Prob. 45ECh. 3.1 - Prob. 46ECh. 3.1 - Prob. 47ECh. 3.1 - Prob. 48ECh. 3.1 - Maximum of a Fourth-Degree Polynomial Find the...Ch. 3.1 - Prob. 50ECh. 3.1 - Prob. 51ECh. 3.1 - Prob. 52ECh. 3.1 - Prob. 53ECh. 3.1 - Sales A soft drink vendor at a popular beach...Ch. 3.1 - Prob. 55ECh. 3.1 - Prob. 56ECh. 3.1 - Prob. 57ECh. 3.1 - Agriculture At a certain vineyard it is found that...Ch. 3.1 - 59-62. Maxima and Minima Use the formulas of the...Ch. 3.1 - Prob. 60ECh. 3.1 - Prob. 61ECh. 3.1 - Prob. 62ECh. 3.1 - Fencing a Horse Corral Carol has 2400 ft of...Ch. 3.1 - Prob. 64ECh. 3.1 - Prob. 65ECh. 3.1 - Prob. 66ECh. 3.1 - Prob. 67ECh. 3.2 - Prob. 1ECh. 3.2 - Prob. 2.1ECh. 3.2 - Prob. 2.2ECh. 3.2 - Prob. 3ECh. 3.2 - Prob. 4ECh. 3.2 - Prob. 5ECh. 3.2 - Prob. 6ECh. 3.2 - Prob. 7ECh. 3.2 - Prob. 8ECh. 3.2 - Prob. 9ECh. 3.2 - Prob. 10ECh. 3.2 - Prob. 11ECh. 3.2 - Prob. 12ECh. 3.2 - Prob. 13ECh. 3.2 - SKILLS 9-14 End behaviour A polynomial function is...Ch. 3.2 - Prob. 15ECh. 3.2 - Prob. 16ECh. 3.2 - Prob. 17ECh. 3.2 - Prob. 18ECh. 3.2 - Prob. 19ECh. 3.2 - Prob. 20ECh. 3.2 - Prob. 21ECh. 3.2 - Prob. 22ECh. 3.2 - Prob. 23ECh. 3.2 - Prob. 24ECh. 3.2 - Prob. 25ECh. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - Prob. 29ECh. 3.2 - Prob. 30ECh. 3.2 - Prob. 31ECh. 3.2 - SKILLS 31-34 Graphing Polynomials Factor the...Ch. 3.2 - Prob. 33ECh. 3.2 - Prob. 34ECh. 3.2 - Prob. 35ECh. 3.2 - Prob. 36ECh. 3.2 - Prob. 37ECh. 3.2 - Prob. 38ECh. 3.2 - Prob. 39ECh. 3.2 - Prob. 40ECh. 3.2 - Prob. 41ECh. 3.2 - Prob. 42ECh. 3.2 - Prob. 43ECh. 3.2 - Prob. 44ECh. 3.2 - Prob. 45ECh. 3.2 - Prob. 46ECh. 3.2 - Prob. 47ECh. 3.2 - Prob. 48ECh. 3.2 - Prob. 49ECh. 3.2 - Prob. 50ECh. 3.2 - Prob. 51ECh. 3.2 - Prob. 52ECh. 3.2 - Prob. 53ECh. 3.2 - Prob. 54ECh. 3.2 - Prob. 55ECh. 3.2 - Prob. 56ECh. 3.2 - Prob. 57ECh. 3.2 - Prob. 58ECh. 3.2 - Prob. 59ECh. 3.2 - Prob. 60ECh. 3.2 - Prob. 61ECh. 3.2 - Prob. 62ECh. 3.2 - Prob. 63ECh. 3.2 - Prob. 64ECh. 3.2 - Prob. 65ECh. 3.2 - Prob. 66ECh. 3.2 - Prob. 67ECh. 3.2 - Prob. 68ECh. 3.2 - Prob. 69ECh. 3.2 - Prob. 70ECh. 3.2 - Prob. 71ECh. 3.2 - Prob. 72ECh. 3.2 - Prob. 73ECh. 3.2 - Prob. 74ECh. 3.2 - Prob. 75ECh. 3.2 - Prob. 76ECh. 3.2 - Prob. 77ECh. 3.2 - Prob. 78ECh. 3.2 - Prob. 79ECh. 3.2 - Prob. 80ECh. 3.2 - Prob. 81ECh. 3.2 - Prob. 82ECh. 3.2 - Prob. 83ECh. 3.2 - Prob. 84ECh. 3.2 - Prob. 85ECh. 3.2 - Prob. 86ECh. 3.2 - Market Research A market analyst working for a...Ch. 3.2 - Prob. 88ECh. 3.2 - Volume of a box An open box is to be constructed...Ch. 3.2 - Volume of a box A cardboard box has a square base,...Ch. 3.2 - Prob. 91ECh. 3.2 - Prob. 92ECh. 3.3 - If we divide the polynomial P by the factor xc and...Ch. 3.3 - a If we divide the polynomial P(x) by the factor...Ch. 3.3 - Prob. 3ECh. 3.3 - 3-8 Division of Polynomials Two polynomials P and...Ch. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - Prob. 9ECh. 3.3 - Prob. 10ECh. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - Prob. 13ECh. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.3 - Prob. 17ECh. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - Prob. 24ECh. 3.3 - Prob. 25ECh. 3.3 - Prob. 26ECh. 3.3 - Prob. 27ECh. 3.3 - Prob. 28ECh. 3.3 - Prob. 29ECh. 3.3 - Prob. 30ECh. 3.3 - Prob. 31ECh. 3.3 - Prob. 32ECh. 3.3 - Prob. 33ECh. 3.3 - Prob. 34ECh. 3.3 - Prob. 35ECh. 3.3 - Prob. 36ECh. 3.3 - Prob. 37ECh. 3.3 - Prob. 38ECh. 3.3 - Prob. 39ECh. 3.3 - Prob. 40ECh. 3.3 - Prob. 41ECh. 3.3 - Prob. 42ECh. 3.3 - Prob. 43ECh. 3.3 - Prob. 44ECh. 3.3 - Prob. 45ECh. 3.3 - Prob. 46ECh. 3.3 - Prob. 47ECh. 3.3 - Prob. 48ECh. 3.3 - Prob. 49ECh. 3.3 - Prob. 50ECh. 3.3 - Prob. 51ECh. 3.3 - Prob. 52ECh. 3.3 - Prob. 53ECh. 3.3 - 53-56 Factor Theorem Use the Factor Theorem to...Ch. 3.3 - Prob. 55ECh. 3.3 - Prob. 56ECh. 3.3 - Prob. 57ECh. 3.3 - Prob. 58ECh. 3.3 - Prob. 59ECh. 3.3 - Prob. 60ECh. 3.3 - Prob. 61ECh. 3.3 - Prob. 62ECh. 3.3 - Prob. 63ECh. 3.3 - Prob. 64ECh. 3.3 - Prob. 65ECh. 3.3 - Prob. 66ECh. 3.3 - Prob. 67ECh. 3.3 - Prob. 68ECh. 3.3 - Prob. 69ECh. 3.3 - Prob. 70ECh. 3.3 - 71-74 Finding a Polynomial from a Graph Find the...Ch. 3.3 - Prob. 72ECh. 3.3 - Prob. 73ECh. 3.3 - Prob. 74ECh. 3.3 - Prob. 75ECh. 3.3 - DISCOVER: Nested Form of a Polynomial Expand Q to...Ch. 3.4 - If the polynomial function...Ch. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 3.4 - 5-10 Possible Rational Zeros List all possible...Ch. 3.4 - Prob. 6ECh. 3.4 - Prob. 7ECh. 3.4 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Prob. 13ECh. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - Prob. 22ECh. 3.4 - Prob. 23ECh. 3.4 - Prob. 24ECh. 3.4 - Prob. 25ECh. 3.4 - Prob. 26ECh. 3.4 - Prob. 27ECh. 3.4 - Prob. 28ECh. 3.4 - Prob. 29ECh. 3.4 - Prob. 30ECh. 3.4 - Prob. 31ECh. 3.4 - Prob. 32ECh. 3.4 - Prob. 33ECh. 3.4 - Prob. 34ECh. 3.4 - Prob. 35ECh. 3.4 - Prob. 36ECh. 3.4 - Prob. 37ECh. 3.4 - Prob. 38ECh. 3.4 - Prob. 39ECh. 3.4 - Prob. 40ECh. 3.4 - Prob. 41ECh. 3.4 - Prob. 42ECh. 3.4 - Prob. 43ECh. 3.4 - Prob. 44ECh. 3.4 - Prob. 45ECh. 3.4 - Prob. 46ECh. 3.4 - Prob. 47ECh. 3.4 - Prob. 48ECh. 3.4 - Prob. 49ECh. 3.4 - 45-54 Real Zeros of a Polynomial Find all the real...Ch. 3.4 - Prob. 51ECh. 3.4 - Prob. 52ECh. 3.4 - Prob. 53ECh. 3.4 - Prob. 54ECh. 3.4 - Prob. 55ECh. 3.4 - Prob. 56ECh. 3.4 - Prob. 57ECh. 3.4 - Prob. 58ECh. 3.4 - Prob. 59ECh. 3.4 - 55-62 Real Zeros of a Polynomial A Polynomial P is...Ch. 3.4 - Prob. 61ECh. 3.4 - Prob. 62ECh. 3.4 - Prob. 63ECh. 3.4 - Prob. 64ECh. 3.4 - Prob. 65ECh. 3.4 - Prob. 66ECh. 3.4 - Prob. 67ECh. 3.4 - Prob. 68ECh. 3.4 - Prob. 69ECh. 3.4 - Prob. 70ECh. 3.4 - Prob. 71ECh. 3.4 - Prob. 72ECh. 3.4 - Prob. 73ECh. 3.4 - Prob. 74ECh. 3.4 - Prob. 75ECh. 3.4 - Prob. 76ECh. 3.4 - Prob. 77ECh. 3.4 - Prob. 78ECh. 3.4 - Prob. 79ECh. 3.4 - Prob. 80ECh. 3.4 - Prob. 81ECh. 3.4 - Prob. 82ECh. 3.4 - Prob. 83ECh. 3.4 - Prob. 84ECh. 3.4 - 81-86 Zeros of a Polynomial Find all rational...Ch. 3.4 - Prob. 86ECh. 3.4 - Prob. 87ECh. 3.4 - Prob. 88ECh. 3.4 - 87-90 Polynomials With No Rational Zeros Show that...Ch. 3.4 - Prob. 90ECh. 3.4 - Prob. 91ECh. 3.4 - Prob. 92ECh. 3.4 - Prob. 93ECh. 3.4 - Prob. 94ECh. 3.4 - Prob. 95ECh. 3.4 - Prob. 96ECh. 3.4 - Prob. 97ECh. 3.4 - Prob. 98ECh. 3.4 - Prob. 99ECh. 3.4 - Prob. 100ECh. 3.4 - Prob. 101ECh. 3.4 - Prob. 102ECh. 3.4 - Prob. 103ECh. 3.4 - Volume of a Box A rectangular box with a volume of...Ch. 3.4 - Girth of a Box A box with a square base has length...Ch. 3.4 - Prob. 106ECh. 3.4 - Prob. 107ECh. 3.4 - Prob. 108ECh. 3.4 - Prob. 109ECh. 3.4 - Prob. 110ECh. 3.5 - Prob. 1ECh. 3.5 - Prob. 2ECh. 3.5 - Prob. 3ECh. 3.5 - Prob. 4ECh. 3.5 - Prob. 5ECh. 3.5 - Prob. 6ECh. 3.5 - Prob. 7ECh. 3.5 - Prob. 8ECh. 3.5 - 7-18. Complete Factorization A polynomial P is...Ch. 3.5 - Prob. 10ECh. 3.5 - Prob. 11ECh. 3.5 - Prob. 12ECh. 3.5 - Prob. 13ECh. 3.5 - Prob. 14ECh. 3.5 - Prob. 15ECh. 3.5 - Prob. 16ECh. 3.5 - Prob. 17ECh. 3.5 - Prob. 18ECh. 3.5 - Prob. 19ECh. 3.5 - Prob. 20ECh. 3.5 - Prob. 21ECh. 3.5 - Prob. 22ECh. 3.5 - Prob. 23ECh. 3.5 - Prob. 24ECh. 3.5 - Prob. 25ECh. 3.5 - Prob. 26ECh. 3.5 - Prob. 27ECh. 3.5 - Prob. 28ECh. 3.5 - Prob. 29ECh. 3.5 - Prob. 30ECh. 3.5 - Prob. 31ECh. 3.5 - Prob. 32ECh. 3.5 - Prob. 33ECh. 3.5 - Prob. 34ECh. 3.5 - Prob. 35ECh. 3.5 - Prob. 36ECh. 3.5 - Prob. 37ECh. 3.5 - Prob. 38ECh. 3.5 - 37-46 Finding a Polynomial with Specified Zeros...Ch. 3.5 - Prob. 40ECh. 3.5 - Prob. 41ECh. 3.5 - Prob. 42ECh. 3.5 - Prob. 43ECh. 3.5 - Prob. 44ECh. 3.5 - 37-46 Finding a Polynomial with Specified Zeros...Ch. 3.5 - Prob. 46ECh. 3.5 - Prob. 47ECh. 3.5 - Prob. 48ECh. 3.5 - Prob. 49ECh. 3.5 - Prob. 50ECh. 3.5 - Prob. 51ECh. 3.5 - Prob. 52ECh. 3.5 - Prob. 53ECh. 3.5 - Prob. 54ECh. 3.5 - Prob. 55ECh. 3.5 - Prob. 56ECh. 3.5 - Prob. 57ECh. 3.5 - Prob. 58ECh. 3.5 - Prob. 59ECh. 3.5 - 47-64 Finding Complex Zeros Find all zeros of the...Ch. 3.5 - Prob. 61ECh. 3.5 - Prob. 62ECh. 3.5 - Prob. 63ECh. 3.5 - Prob. 64ECh. 3.5 - Prob. 65ECh. 3.5 - Prob. 66ECh. 3.5 - Prob. 67ECh. 3.5 - Prob. 68ECh. 3.5 - Prob. 69ECh. 3.5 - Prob. 70ECh. 3.5 - Prob. 71ECh. 3.5 - Prob. 72ECh. 3.5 - Prob. 73ECh. 3.5 - Prob. 74ECh. 3.5 - Prob. 75ECh. 3.5 - Prob. 76ECh. 3.6 - If the rational function y=r(x) has the vertical...Ch. 3.6 - If the rational function y=r(x) has the horizontal...Ch. 3.6 - 3-6 The following questions are about the rational...Ch. 3.6 - Prob. 4ECh. 3.6 - Prob. 5ECh. 3.6 - Prob. 6ECh. 3.6 - Prob. 7ECh. 3.6 - Prob. 8ECh. 3.6 - Prob. 9ECh. 3.6 - Prob. 10ECh. 3.6 - Prob. 11ECh. 3.6 - Prob. 12ECh. 3.6 - Prob. 13ECh. 3.6 - Prob. 14ECh. 3.6 - Prob. 15ECh. 3.6 - Prob. 16ECh. 3.6 - Prob. 17ECh. 3.6 - Prob. 18ECh. 3.6 - Prob. 19ECh. 3.6 - Prob. 20ECh. 3.6 - Prob. 21ECh. 3.6 - Prob. 22ECh. 3.6 - Prob. 23ECh. 3.6 - Prob. 24ECh. 3.6 - Prob. 25ECh. 3.6 - Prob. 26ECh. 3.6 - Prob. 27ECh. 3.6 - Prob. 28ECh. 3.6 - Prob. 29ECh. 3.6 - Prob. 30ECh. 3.6 - Prob. 31ECh. 3.6 - Prob. 32ECh. 3.6 - Prob. 33ECh. 3.6 - Prob. 34ECh. 3.6 - Prob. 35ECh. 3.6 - Prob. 36ECh. 3.6 - Prob. 37ECh. 3.6 - Prob. 38ECh. 3.6 - Prob. 39ECh. 3.6 - Prob. 40ECh. 3.6 - Prob. 41ECh. 3.6 - Prob. 42ECh. 3.6 - Prob. 43ECh. 3.6 - Prob. 44ECh. 3.6 - Prob. 45ECh. 3.6 - Prob. 46ECh. 3.6 - Prob. 47ECh. 3.6 - Prob. 48ECh. 3.6 - Prob. 49ECh. 3.6 - Prob. 50ECh. 3.6 - Prob. 51ECh. 3.6 - Prob. 52ECh. 3.6 - Prob. 53ECh. 3.6 - Prob. 54ECh. 3.6 - Prob. 55ECh. 3.6 - Prob. 56ECh. 3.6 - Prob. 57ECh. 3.6 - Prob. 58ECh. 3.6 - Prob. 59ECh. 3.6 - Prob. 60ECh. 3.6 - Prob. 61ECh. 3.6 - Prob. 62ECh. 3.6 - Prob. 63ECh. 3.6 - Prob. 64ECh. 3.6 - Prob. 65ECh. 3.6 - Prob. 66ECh. 3.6 - Prob. 67ECh. 3.6 - 63-68 Rational Functions with Holes Find the...Ch. 3.6 - Prob. 69ECh. 3.6 - Prob. 70ECh. 3.6 - Prob. 71ECh. 3.6 - Prob. 72ECh. 3.6 - Prob. 73ECh. 3.6 - Prob. 74ECh. 3.6 - Prob. 75ECh. 3.6 - Prob. 76ECh. 3.6 - Prob. 77ECh. 3.6 - Prob. 78ECh. 3.6 - Prob. 79ECh. 3.6 - Prob. 80ECh. 3.6 - Prob. 81ECh. 3.6 - 81-86 End Behavior Graph the rational function,...Ch. 3.6 - Prob. 83ECh. 3.6 - Prob. 84ECh. 3.6 - Prob. 85ECh. 3.6 - Prob. 86ECh. 3.6 - Prob. 87ECh. 3.6 - Drug Concentration After a certain drug is...Ch. 3.6 - Drug Concentration A drug is administered to a...Ch. 3.6 - Prob. 90ECh. 3.6 - Prob. 91ECh. 3.6 - Focusing Distance For a camera with a lens of...Ch. 3.6 - DISCUSS: Constructing a Rational Function from its...Ch. 3.6 - DISCUSS: A Rational Function with No Asymptote...Ch. 3.6 - Prob. 95ECh. 3.7 - Concepts To solve a polynomial inequality, we...Ch. 3.7 - Prob. 2ECh. 3.7 - Prob. 3ECh. 3.7 - Prob. 4ECh. 3.7 - Prob. 5ECh. 3.7 - Prob. 6ECh. 3.7 - Prob. 7ECh. 3.7 - Prob. 8ECh. 3.7 - Prob. 9ECh. 3.7 - Prob. 10ECh. 3.7 - Prob. 11ECh. 3.7 - Prob. 12ECh. 3.7 - Prob. 13ECh. 3.7 - Prob. 14ECh. 3.7 - Prob. 15ECh. 3.7 - Prob. 16ECh. 3.7 - Prob. 17ECh. 3.7 - Prob. 18ECh. 3.7 - Prob. 19ECh. 3.7 - Prob. 20ECh. 3.7 - Prob. 21ECh. 3.7 - Prob. 22ECh. 3.7 - Prob. 23ECh. 3.7 - Prob. 24ECh. 3.7 - Prob. 25ECh. 3.7 - Prob. 26ECh. 3.7 - Prob. 27ECh. 3.7 - Prob. 28ECh. 3.7 - Prob. 29ECh. 3.7 - Prob. 30ECh. 3.7 - Prob. 31ECh. 3.7 - Prob. 32ECh. 3.7 - Prob. 33ECh. 3.7 - Prob. 34ECh. 3.7 - Prob. 35ECh. 3.7 - Prob. 36ECh. 3.7 - Prob. 37ECh. 3.7 - Prob. 38ECh. 3.7 - Prob. 39ECh. 3.7 - Prob. 40ECh. 3.7 - Prob. 41ECh. 3.7 - Prob. 42ECh. 3.7 - Prob. 43ECh. 3.7 - Prob. 44ECh. 3.7 - Prob. 45ECh. 3.7 - Prob. 46ECh. 3.7 - Prob. 47ECh. 3.7 - Prob. 48ECh. 3.7 - Prob. 49ECh. 3.7 - Prob. 50ECh. 3.7 - Prob. 51ECh. 3.7 - SKILLS Plus 51-52. Rational Inequalities Solve the...Ch. 3.7 - Prob. 53ECh. 3.7 - General Rational Inequality Solve the inequality...Ch. 3.7 - Prob. 55ECh. 3.7 - Prob. 56ECh. 3.7 - Prob. 57ECh. 3.7 - Prob. 58ECh. 3.CR - Prob. 1CCCh. 3.CR - Prob. 2CCCh. 3.CR - Prob. 3CCCh. 3.CR - Prob. 4CCCh. 3.CR - Prob. 5CCCh. 3.CR - Prob. 6CCCh. 3.CR - Prob. 7CCCh. 3.CR - Prob. 8CCCh. 3.CR - Prob. 9CCCh. 3.CR - Prob. 10CCCh. 3.CR - Prob. 11CCCh. 3.CR - Prob. 12CCCh. 3.CR - Prob. 13CCCh. 3.CR - Prob. 14CCCh. 3.CR - Prob. 1ECh. 3.CR - Prob. 2ECh. 3.CR - Prob. 3ECh. 3.CR - Prob. 4ECh. 3.CR - Prob. 5ECh. 3.CR - Prob. 6ECh. 3.CR - Prob. 7ECh. 3.CR - Prob. 8ECh. 3.CR - Prob. 9ECh. 3.CR - Prob. 10ECh. 3.CR - Prob. 11ECh. 3.CR - Prob. 12ECh. 3.CR - Prob. 13ECh. 3.CR - Prob. 14ECh. 3.CR - Prob. 15ECh. 3.CR - Prob. 16ECh. 3.CR - Prob. 17ECh. 3.CR - Prob. 18ECh. 3.CR - Prob. 19ECh. 3.CR - Prob. 20ECh. 3.CR - 21-24- Graphing polynomials: Use a graphing device...Ch. 3.CR - Prob. 22ECh. 3.CR - Prob. 23ECh. 3.CR - Prob. 24ECh. 3.CR - Strength of a Beam The strength S of a wooden beam...Ch. 3.CR - Prob. 26ECh. 3.CR - Prob. 27ECh. 3.CR - Prob. 28ECh. 3.CR - Prob. 29ECh. 3.CR - Prob. 30ECh. 3.CR - Prob. 31ECh. 3.CR - Prob. 32ECh. 3.CR - Prob. 33ECh. 3.CR - Prob. 34ECh. 3.CR - Prob. 35ECh. 3.CR - Prob. 36ECh. 3.CR - Prob. 37ECh. 3.CR - Prob. 38ECh. 3.CR - Prob. 39ECh. 3.CR - Prob. 40ECh. 3.CR - Prob. 41ECh. 3.CR - Prob. 42ECh. 3.CR - Prob. 43ECh. 3.CR - Prob. 44ECh. 3.CR - Prob. 45ECh. 3.CR - Prob. 46ECh. 3.CR - Prob. 47ECh. 3.CR - Prob. 48ECh. 3.CR - Prob. 49ECh. 3.CR - Prob. 50ECh. 3.CR - Prob. 51ECh. 3.CR - Prob. 52ECh. 3.CR - Prob. 53ECh. 3.CR - Prob. 54ECh. 3.CR - Prob. 55ECh. 3.CR - Prob. 56ECh. 3.CR - Prob. 57ECh. 3.CR - Prob. 58ECh. 3.CR - Prob. 59ECh. 3.CR - Prob. 60ECh. 3.CR - Prob. 61ECh. 3.CR - Prob. 62ECh. 3.CR - Prob. 63ECh. 3.CR - Prob. 64ECh. 3.CR - Prob. 65ECh. 3.CR - Prob. 66ECh. 3.CR - Prob. 67ECh. 3.CR - Prob. 68ECh. 3.CR - Prob. 69ECh. 3.CR - Prob. 70ECh. 3.CR - Prob. 71ECh. 3.CR - Prob. 72ECh. 3.CR - Prob. 73ECh. 3.CR - Prob. 74ECh. 3.CR - Prob. 75ECh. 3.CR - Prob. 76ECh. 3.CR - Prob. 77ECh. 3.CR - Prob. 78ECh. 3.CR - Prob. 79ECh. 3.CR - Prob. 80ECh. 3.CR - Prob. 81ECh. 3.CR - Prob. 82ECh. 3.CR - Prob. 83ECh. 3.CR - Prob. 84ECh. 3.CR - Prob. 85ECh. 3.CR - Prob. 86ECh. 3.CR - Prob. 87ECh. 3.CR - Prob. 88ECh. 3.CR - Prob. 89ECh. 3.CR - Prob. 90ECh. 3.CR - Prob. 91ECh. 3.CR - Prob. 92ECh. 3.CR - Prob. 93ECh. 3.CR - Prob. 94ECh. 3.CR - Prob. 95ECh. 3.CR - Prob. 96ECh. 3.CR - Prob. 97ECh. 3.CR - Prob. 98ECh. 3.CR - Prob. 99ECh. 3.CR - Prob. 100ECh. 3.CR - Prob. 101ECh. 3.CR - Prob. 102ECh. 3.CR - Prob. 103ECh. 3.CR - Prob. 104ECh. 3.CR - Prob. 105ECh. 3.CR - Prob. 106ECh. 3.CT - Prob. 1CTCh. 3.CT - Find the maximum or minimum value of the quadratic...Ch. 3.CT - A cannonball fired out to sea from a shore battery...Ch. 3.CT - Graph the polynomial P(x)=(x+2)3+27, showing...Ch. 3.CT - Prob. 5CTCh. 3.CT - Prob. 6CTCh. 3.CT - Prob. 7CTCh. 3.CT - Prob. 8CTCh. 3.CT - Prob. 9CTCh. 3.CT - Prob. 10CTCh. 3.CT - Prob. 11CTCh. 3.CT - Prob. 12CTCh. 3.CT - Prob. 13CTCh. 3.CT - Prob. 14CTCh. 3.FOM - PROBLEMS Tire inflation and Treadwear Car tires...Ch. 3.FOM - Prob. 2PCh. 3.FOM - PROBLEMS How Fast Can You List Your Favourite...Ch. 3.FOM - PROBLEMS Height of a Baseball A baseball is thrown...Ch. 3.FOM - PROBLEMS Torricellis Law Water in a tank flow out...
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- - 1 For the function F(x) = (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. %3D x + 8x + 16 (Type an integer or a simplified fraction.) C. The domain of the given function is {x|x is a real number, x+ - 4 }. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) D. The domain of the given function is the set of all real numbers. What is the range of the given function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. }. A. The range of the given function is {yly is a real number, y> (Type an integer or a simplified fraction.) }. B. The range of the given function is {yly is a real number, y + (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) C. The range of the given function is {yly is a real number, y< 0}. (Type an integer…arrow_forward20,000(x - 14) The rational function f(x) 3D 8x models the number of arrests, f(x), per 100,000 drivers, for driving under the influence of alcohol, as a function of a x2 – 9 driver's age, x. Complete parts (a) through (c). a. Graph the function in a [0,70,5] by [0,400,20] viewing rectangle. Choose the correct graph below. OA. OB. OC. OD. b. Describe the trend shown by the graph. O A. The graph shows a rapid increase as x approaches a maximum in the lower half of the domain, and a gradual decrease as x increases past the maximum. O B. The graph shows a rapid increase as x approaches a maximum in the upper half of the domain, and a gradual decrease as x increases past the maximum. O C. The graph shows a gradual increase as x approaches a maximum the lower half of the domain, and a rapid decrease as x increases past the maximum. c. Use the ZOOM and TRACE features or the maximum function feature of your graphing utility to find the age that corresponds to the greatest number of arrests.…arrow_forwardEXAMPLE 6 Graphing a Rational Function x² – 4 2x2 + 2x Graph the rational function r(x) and state the domain and range. %3Darrow_forward
- 1 For the function F(x) = - 7+- (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. (a) Choose the correct graph below, cei O A. OB. OC. OD. e A As (b) What is the domain of the given function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The domain of the given function is {x)x is a real number, x#} (Type an integer or a simplified fraction. Use a comma to separate answers as needed, ) O B. The domain of the given function is (x)x is a real number, x> (Type an integer or a simplified fraction.) O C. The domain of the given fupction is x|x is a real number, x} (Type an integer or a simplified fraction.) mpleted O D. The range of the given function is the set of all real numbers. (c) What is/are the vertical asymptote(s)? Select the correct choice below and, if necessary, fill in the…arrow_forward- 2 (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. For the function H(x) = x+4' (a) Choose the correct graph below. O A. В. OC. D. 20- Ay 20- 20- 20- -20 20 -20 -20 20 -20 20 20 (b) What is the domain of the given function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The domain of the given function is {x|x is a real number, x> }. (Type an integer or a simplified fraction.) B. The domain of the given function is {x|x is a real number, x }. (Type an integer or a simplified fraction.) O B. The range of the given function is {yly is a real number, y< }. (Type an integer or a simplified fraction.) O C. The range of the given function is {yly is a real number, y# }. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) D. The range of the given function…arrow_forward8) Graph the rational function R(x) = using transformations. Determine the (х-3)2 domain, range, asymptotes, and intercepts.arrow_forward
- EXAMPLE 8 Graphing a Rational Function 4x Graph f(x) x - 4arrow_forwardThe function g is related to one of the parent functions described in an earlier section. g(x) = -√x+2 -1 (a) Identify the parent function f. f(x) = (b) Describe the sequence of transformations from f to g. (Select all that apply.) horizontal shift of 2 units to the right reflection in the x-axis Ⓒhorizontal shift of 2 units to the left Overtical shrink vertical shift of 1 unit downward (c) Sketch the graph of g. 19 La y 2 165 + 2- (d) Use function notation to write g in terms of f. g(x) = + 2 -6 y y 2- 4-arrow_forwardThink about rational functions. Sketch a graph by hand of a possible rational functions. Identify the following from your graph: Domain x-intercepts. y-intercept. horizontal asymptotes. vertical asymptotes.arrow_forward
- Graph the functions on the same screen using the given viewing rectangle. Viewing rectangle [−8, 8] by [−2, 8](a) y = 4 x (b) y = 4 x + 6 (c) y = 2 4 x + 6 (d) y = 3 + 2 4 x + 6 How is the graph in part (b) related to the graph in part (a)? If a graph is not supposed to be stretched or shrunk, enter "1" in the corresponding box on the right. If a graph is not supposed to be shifted in some direction, enter "0" in the corresponding box on the right.arrow_forwardFor the function F(x) = (x – 6)2 (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. (Type an integer or a simplified fraction.) D. The domain of the given function is the set of all real numbers. What is the range of the given function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The range of the given function is {yly is a real number, y+ }. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. The range of the given function is {yly is a real number, y> 0}. (Type an integer or a simplified fraction.) The range of the given function is {yly is a real number, y< }. (Type an integer or a simplified fraction.) D. The range of the given function is the set of all real numbers. (c) What is/are the vertical asymptote(s)? Select the correct choice below and,…arrow_forwardThe function g is related to one of the parent functions described in an earlier section. 9(x) = √3x +4 (a) Identify the parent function f. f(x)=√x (b) Describe the sequence of transformations from fto g. (Select all that apply.) ✔horizontal shift of 4 units to the right vertical shift of 4 units downward vertical shrink vertical shift of 4 units upward ✔horizontal shrink (c) Sketch the graph of g. O -5 y X 10 5 -10 y 10 5 -10 (d) Use function notation to write g in terms of f. 9(x)=√3√√x + 4 5 5 X x -5 -5 10 -10 y 10 5 -10 5 Xarrow_forward
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