EBK ALGEBRA 2
EBK ALGEBRA 2
11th Edition
ISBN: 9780544714304
Author: Larson
Publisher: HMH PUB
Expert Solution & Answer
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Chapter 5.3, Problem 15E
Solution

To graph : The given function.

Given information :

Function y=2xx2−1

Graph :

  EBK ALGEBRA 2, Chapter 5.3, Problem 15E

Interpretation :

The numerator is zero when x=0 , so the x  and  y -intercept is at (0,0) .

As x→+∞ the denominator approaches +∞ while the numerator is positive so y approaches zero from above the x axis and there is a horizontal asymptote is y=0 .

As x→−∞ the denominator approaches +∞ while the numerator is negative so y approaches zero from below the x axis and the same horizontal asymptote is y=0 .

The zeros of the denominator are the vertical asymptotes.

  0  =x2−1 0 =(x+1)(x−2)x =−1,1

Calculate some points, especially some close to the vertical asymptotes to see which way the graph goes.

    xf(x)
    −5.0−0.42
    −4.0−0.53
    −3.0−0.75
    −2.0−1.33
    −1.5−2.40
    −1.4−2.92
    −1.3−3.77
    −1.2−5.45
    −1.1−10.48
    −0.99.47
    −0.84.44
    −0.72.75
    −0.61.87
    0.00.00
    0.5−1.33
    0.6−1.88
    0.7−2.75
    0.8−4.44
    0.9−9.47
    1.110.48
    1.25.45
    1.33.77
    1.42.92
    1.52.40
    2.01.33
    3.00.75
    4.00.53
    5.00.42

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Chapter 5.3, Problem 14E
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Chapter 5.3, Problem 16E

Chapter 5 Solutions

EBK ALGEBRA 2

Ch. 5.1 - Prob. 1GPCh. 5.1 - Prob. 2GPCh. 5.1 - Prob. 3GPCh. 5.1 - Prob. 4GPCh. 5.1 - Prob. 5GPCh. 5.1 - Prob. 6GPCh. 5.1 - Prob. 7GPCh. 5.1 - Prob. 8GPCh. 5.1 - Prob. 9GPCh. 5.1 - Prob. 10GP
Ch. 5.1 - Prob. 11GPCh. 5.1 - Prob. 12GPCh. 5.1 - Prob. 13GPCh. 5.1 - Prob. 14GPCh. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10ECh. 5.1 - Prob. 11ECh. 5.1 - Prob. 12ECh. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - Prob. 18ECh. 5.1 - Prob. 19ECh. 5.1 - Prob. 20ECh. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - Prob. 25ECh. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - Prob. 33ECh. 5.1 - Prob. 34ECh. 5.1 - Prob. 35ECh. 5.1 - Prob. 36ECh. 5.1 - Prob. 37PSCh. 5.1 - Prob. 38PSCh. 5.1 - Prob. 39PSCh. 5.1 - Prob. 40PSCh. 5.1 - Prob. 41PSCh. 5.1 - Prob. 42PSCh. 5.2 - Prob. 1GPCh. 5.2 - Prob. 2GPCh. 5.2 - Prob. 3GPCh. 5.2 - Prob. 4GPCh. 5.2 - Prob. 5GPCh. 5.2 - Prob. 6GPCh. 5.2 - Prob. 7GPCh. 5.2 - Prob. 1ECh. 5.2 - Prob. 2ECh. 5.2 - Prob. 3ECh. 5.2 - Prob. 4ECh. 5.2 - Prob. 5ECh. 5.2 - Prob. 6ECh. 5.2 - Prob. 7ECh. 5.2 - Prob. 8ECh. 5.2 - Prob. 9ECh. 5.2 - Prob. 10ECh. 5.2 - Prob. 11ECh. 5.2 - Prob. 12ECh. 5.2 - Prob. 13ECh. 5.2 - Prob. 14ECh. 5.2 - Prob. 15ECh. 5.2 - Prob. 16ECh. 5.2 - Prob. 17ECh. 5.2 - Prob. 18ECh. 5.2 - Prob. 19ECh. 5.2 - Prob. 20ECh. 5.2 - Prob. 21ECh. 5.2 - Prob. 22ECh. 5.2 - Prob. 23ECh. 5.2 - Prob. 24ECh. 5.2 - Prob. 25ECh. 5.2 - Prob. 26ECh. 5.2 - Prob. 27ECh. 5.2 - Prob. 28ECh. 5.2 - Prob. 29ECh. 5.2 - Prob. 30ECh. 5.2 - Prob. 31ECh. 5.2 - Prob. 32ECh. 5.2 - Prob. 33ECh. 5.2 - Prob. 34ECh. 5.2 - Prob. 35ECh. 5.2 - Prob. 36ECh. 5.2 - Prob. 37PSCh. 5.2 - Prob. 38PSCh. 5.2 - Prob. 39PSCh. 5.2 - Prob. 40PSCh. 5.2 - Prob. 41PSCh. 5.2 - Prob. 42PSCh. 5.2 - Prob. 1PCh. 5.2 - Prob. 2PCh. 5.2 - Prob. 3PCh. 5.2 - Prob. 4PCh. 5.2 - Prob. 5PCh. 5.2 - Prob. 6PCh. 5.2 - Prob. 7PCh. 5.2 - Prob. 8PCh. 5.2 - Prob. 9PCh. 5.2 - Prob. 1.1PCh. 5.2 - Prob. 1.2PCh. 5.2 - Prob. 1.3PCh. 5.2 - Prob. 1.4PCh. 5.2 - Prob. 1.5PCh. 5.2 - Prob. 1.6PCh. 5.2 - Prob. 1.7PCh. 5.2 - Prob. 1.8PCh. 5.2 - Prob. 1.9PCh. 5.2 - Prob. 1.10PCh. 5.3 - Prob. 1GPCh. 5.3 - Prob. 2GPCh. 5.3 - Prob. 3GPCh. 5.3 - Prob. 4GPCh. 5.3 - Prob. 5GPCh. 5.3 - Prob. 1ECh. 5.3 - Prob. 2ECh. 5.3 - Prob. 3ECh. 5.3 - Prob. 4ECh. 5.3 - Prob. 5ECh. 5.3 - Prob. 6ECh. 5.3 - Prob. 7ECh. 5.3 - Prob. 8ECh. 5.3 - Prob. 9ECh. 5.3 - Prob. 10ECh. 5.3 - Prob. 11ECh. 5.3 - Prob. 12ECh. 5.3 - Prob. 13ECh. 5.3 - Prob. 14ECh. 5.3 - Prob. 15ECh. 5.3 - Prob. 16ECh. 5.3 - Prob. 17ECh. 5.3 - Prob. 18ECh. 5.3 - Prob. 19ECh. 5.3 - Prob. 20ECh. 5.3 - Prob. 21ECh. 5.3 - Prob. 22ECh. 5.3 - Prob. 23ECh. 5.3 - Prob. 24ECh. 5.3 - Prob. 25ECh. 5.3 - Prob. 26ECh. 5.3 - Prob. 27ECh. 5.3 - Prob. 28ECh. 5.3 - Prob. 29ECh. 5.3 - Prob. 30ECh. 5.3 - Prob. 31PSCh. 5.3 - Prob. 32PSCh. 5.3 - Prob. 33PSCh. 5.3 - Prob. 34PSCh. 5.3 - Prob. 35PSCh. 5.3 - Prob. 36PSCh. 5.3 - Prob. 1QCh. 5.3 - Prob. 2QCh. 5.3 - Prob. 3QCh. 5.3 - Prob. 4QCh. 5.3 - Prob. 5QCh. 5.3 - Prob. 6QCh. 5.3 - Prob. 7QCh. 5.3 - Prob. 8QCh. 5.3 - Prob. 9QCh. 5.3 - Prob. 10QCh. 5.3 - Prob. 11QCh. 5.3 - Prob. 1MRPSCh. 5.3 - Prob. 2MRPSCh. 5.3 - Prob. 3MRPSCh. 5.3 - Prob. 4MRPSCh. 5.3 - Prob. 5MRPSCh. 5.3 - Prob. 6MRPSCh. 5.3 - Prob. 7MRPSCh. 5.3 - Prob. 8MRPSCh. 5.4 - Prob. 1GPCh. 5.4 - Prob. 2GPCh. 5.4 - Prob. 3GPCh. 5.4 - Prob. 4GPCh. 5.4 - Prob. 5GPCh. 5.4 - Prob. 6GPCh. 5.4 - Prob. 7GPCh. 5.4 - Prob. 8GPCh. 5.4 - Prob. 9GPCh. 5.4 - Prob. 10GPCh. 5.4 - Prob. 11GPCh. 5.4 - Prob. 12GPCh. 5.4 - Prob. 1ECh. 5.4 - Prob. 2ECh. 5.4 - Prob. 3ECh. 5.4 - Prob. 4ECh. 5.4 - Prob. 5ECh. 5.4 - Prob. 6ECh. 5.4 - Prob. 7ECh. 5.4 - Prob. 8ECh. 5.4 - Prob. 9ECh. 5.4 - Prob. 10ECh. 5.4 - Prob. 11ECh. 5.4 - Prob. 12ECh. 5.4 - Prob. 13ECh. 5.4 - Prob. 14ECh. 5.4 - Prob. 15ECh. 5.4 - Prob. 16ECh. 5.4 - Prob. 17ECh. 5.4 - Prob. 18ECh. 5.4 - Prob. 19ECh. 5.4 - Prob. 20ECh. 5.4 - Prob. 21ECh. 5.4 - Prob. 22ECh. 5.4 - Prob. 23ECh. 5.4 - Prob. 24ECh. 5.4 - Prob. 25ECh. 5.4 - Prob. 26ECh. 5.4 - Prob. 27ECh. 5.4 - Prob. 28ECh. 5.4 - Prob. 29ECh. 5.4 - Prob. 30ECh. 5.4 - Prob. 31ECh. 5.4 - Prob. 32ECh. 5.4 - Prob. 33ECh. 5.4 - Prob. 34ECh. 5.4 - Prob. 35ECh. 5.4 - Prob. 36ECh. 5.4 - Prob. 37ECh. 5.4 - Prob. 38ECh. 5.4 - Prob. 39ECh. 5.4 - Prob. 40ECh. 5.4 - Prob. 41ECh. 5.4 - Prob. 42ECh. 5.4 - Prob. 43ECh. 5.4 - Prob. 44ECh. 5.4 - Prob. 45ECh. 5.4 - Prob. 46ECh. 5.4 - Prob. 47ECh. 5.4 - Prob. 48PSCh. 5.4 - Prob. 49PSCh. 5.4 - Prob. 50PSCh. 5.4 - Prob. 51PSCh. 5.4 - Prob. 52PSCh. 5.4 - Prob. 53PSCh. 5.4 - Prob. 1PCh. 5.4 - Prob. 2PCh. 5.4 - Prob. 3PCh. 5.4 - Prob. 4PCh. 5.4 - Prob. 5PCh. 5.4 - Prob. 6PCh. 5.5 - Prob. 1GPCh. 5.5 - Prob. 2GPCh. 5.5 - Prob. 3GPCh. 5.5 - Prob. 4GPCh. 5.5 - Prob. 5GPCh. 5.5 - Prob. 6GPCh. 5.5 - Prob. 7GPCh. 5.5 - Prob. 8GPCh. 5.5 - Prob. 9GPCh. 5.5 - Prob. 10GPCh. 5.5 - Prob. 11GPCh. 5.5 - Prob. 12GPCh. 5.5 - Prob. 13GPCh. 5.5 - Prob. 1ECh. 5.5 - Prob. 2ECh. 5.5 - Prob. 3ECh. 5.5 - Prob. 4ECh. 5.5 - Prob. 5ECh. 5.5 - Prob. 6ECh. 5.5 - Prob. 7ECh. 5.5 - Prob. 8ECh. 5.5 - Prob. 9ECh. 5.5 - Prob. 10ECh. 5.5 - Prob. 11ECh. 5.5 - Prob. 12ECh. 5.5 - Prob. 13ECh. 5.5 - Prob. 14ECh. 5.5 - Prob. 15ECh. 5.5 - Prob. 16ECh. 5.5 - Prob. 17ECh. 5.5 - Prob. 18ECh. 5.5 - Prob. 19ECh. 5.5 - Prob. 20ECh. 5.5 - Prob. 21ECh. 5.5 - Prob. 22ECh. 5.5 - Prob. 23ECh. 5.5 - Prob. 24ECh. 5.5 - Prob. 25ECh. 5.5 - Prob. 26ECh. 5.5 - Prob. 27ECh. 5.5 - Prob. 28ECh. 5.5 - Prob. 29ECh. 5.5 - Prob. 30ECh. 5.5 - Prob. 31ECh. 5.5 - Prob. 32ECh. 5.5 - Prob. 33ECh. 5.5 - Prob. 34ECh. 5.5 - Prob. 35ECh. 5.5 - Prob. 36ECh. 5.5 - Prob. 37ECh. 5.5 - Prob. 38ECh. 5.5 - Prob. 39ECh. 5.5 - Prob. 40ECh. 5.5 - Prob. 41PSCh. 5.5 - Prob. 42PSCh. 5.5 - Prob. 43PSCh. 5.5 - Prob. 44PSCh. 5.5 - Prob. 45PSCh. 5.5 - Prob. 1PCh. 5.5 - Prob. 2PCh. 5.5 - Prob. 3PCh. 5.5 - Prob. 4PCh. 5.5 - Prob. 5PCh. 5.5 - Prob. 6PCh. 5.5 - Prob. 7PCh. 5.6 - Prob. 1GPCh. 5.6 - Prob. 2GPCh. 5.6 - Prob. 3GPCh. 5.6 - Prob. 4GPCh. 5.6 - Prob. 5GPCh. 5.6 - Prob. 6GPCh. 5.6 - Prob. 7GPCh. 5.6 - Prob. 8GPCh. 5.6 - Prob. 9GPCh. 5.6 - Prob. 10GPCh. 5.6 - Prob. 11GPCh. 5.6 - Prob. 1ECh. 5.6 - Prob. 2ECh. 5.6 - Prob. 3ECh. 5.6 - Prob. 4ECh. 5.6 - Prob. 5ECh. 5.6 - Prob. 6ECh. 5.6 - Prob. 7ECh. 5.6 - Prob. 8ECh. 5.6 - Prob. 9ECh. 5.6 - Prob. 10ECh. 5.6 - Prob. 11ECh. 5.6 - Prob. 12ECh. 5.6 - Prob. 13ECh. 5.6 - Prob. 14ECh. 5.6 - Prob. 15ECh. 5.6 - Prob. 16ECh. 5.6 - Prob. 17ECh. 5.6 - Prob. 18ECh. 5.6 - Prob. 19ECh. 5.6 - Prob. 20ECh. 5.6 - Prob. 21ECh. 5.6 - Prob. 22ECh. 5.6 - Prob. 23ECh. 5.6 - Prob. 24ECh. 5.6 - Prob. 25ECh. 5.6 - Prob. 26ECh. 5.6 - Prob. 27ECh. 5.6 - Prob. 28ECh. 5.6 - Prob. 29ECh. 5.6 - Prob. 30ECh. 5.6 - Prob. 31ECh. 5.6 - Prob. 32ECh. 5.6 - Prob. 33PSCh. 5.6 - Prob. 34PSCh. 5.6 - Prob. 35PSCh. 5.6 - Prob. 36PSCh. 5.6 - Prob. 37PSCh. 5.6 - Prob. 38PSCh. 5.6 - Prob. 1QCh. 5.6 - Prob. 2QCh. 5.6 - Prob. 3QCh. 5.6 - Prob. 4QCh. 5.6 - Prob. 5QCh. 5.6 - Prob. 6QCh. 5.6 - Prob. 7QCh. 5.6 - Prob. 8QCh. 5.6 - Prob. 9QCh. 5.6 - Prob. 10QCh. 5.6 - Prob. 11QCh. 5.6 - Prob. 12QCh. 5.6 - Prob. 13QCh. 5.6 - Prob. 14QCh. 5.6 - Prob. 1PCh. 5.6 - Prob. 2PCh. 5.6 - Prob. 3PCh. 5.6 - Prob. 4PCh. 5.6 - Prob. 5PCh. 5.6 - Prob. 6PCh. 5.6 - Prob. 7PCh. 5.6 - Prob. 1.1PCh. 5.6 - Prob. 1.2PCh. 5.6 - Prob. 1.3PCh. 5.6 - Prob. 1.4PCh. 5.6 - Prob. 1.5PCh. 5.6 - Prob. 1.6PCh. 5.6 - Prob. 1.7PCh. 5.6 - Prob. 1.8PCh. 5.6 - Prob. 1.9PCh. 5.6 - Prob. 1.10PCh. 5.6 - Prob. 1.11PCh. 5.6 - Prob. 1.12PCh. 5.6 - Prob. 1.13PCh. 5.6 - Prob. 1.14PCh. 5.6 - Prob. 1.15PCh. 5.6 - Prob. 1.16PCh. 5.6 - Prob. 1.17PCh. 5.6 - Prob. 1.18PCh. 5.6 - Prob. 1.19PCh. 5.6 - Prob. 1.20PCh. 5.6 - Prob. 1.21PCh. 5.6 - Prob. 1.22PCh. 5.7 - Prob. 1GPCh. 5.7 - Prob. 2GPCh. 5.7 - Prob. 3GPCh. 5.7 - Prob. 4GPCh. 5.7 - Prob. 5GPCh. 5.7 - Prob. 1ECh. 5.7 - Prob. 2ECh. 5.7 - Prob. 3ECh. 5.7 - Prob. 4ECh. 5.7 - Prob. 5ECh. 5.7 - Prob. 6ECh. 5.7 - Prob. 7ECh. 5.7 - Prob. 8ECh. 5.7 - Prob. 9ECh. 5.7 - Prob. 10ECh. 5.7 - Prob. 11ECh. 5.7 - Prob. 12ECh. 5.7 - Prob. 13ECh. 5.7 - Prob. 14ECh. 5.7 - Prob. 15ECh. 5.7 - Prob. 16ECh. 5.7 - Prob. 17ECh. 5.7 - Prob. 18ECh. 5.7 - Prob. 19ECh. 5.7 - Prob. 20ECh. 5.7 - Prob. 21ECh. 5.7 - Prob. 22ECh. 5.7 - Prob. 23ECh. 5.7 - Prob. 24ECh. 5.7 - Prob. 25ECh. 5.7 - Prob. 26PSCh. 5.7 - Prob. 27PSCh. 5.7 - Prob. 28PSCh. 5.7 - Prob. 29PSCh. 5.7 - Prob. 30PSCh. 5.7 - Prob. 31PSCh. 5.7 - Prob. 32PSCh. 5.7 - Prob. 1QCh. 5.7 - Prob. 2QCh. 5.7 - Prob. 3QCh. 5.7 - Prob. 4QCh. 5.7 - Prob. 5QCh. 5.7 - Prob. 1MRPSCh. 5.7 - Prob. 2MRPSCh. 5.7 - Prob. 3MRPSCh. 5.7 - Prob. 4MRPSCh. 5.7 - Prob. 5MRPSCh. 5.7 - Prob. 6MRPSCh. 5.7 - Prob. 7MRPSCh. 5 - Prob. 1VECh. 5 - Prob. 2VECh. 5 - Prob. 3VECh. 5 - Prob. 4VECh. 5 - Prob. 5VECh. 5 - Prob. 6REAECh. 5 - Prob. 7REAECh. 5 - Prob. 8REAECh. 5 - Prob. 9REAECh. 5 - Prob. 10REAECh. 5 - Prob. 11REAECh. 5 - Prob. 12REAECh. 5 - Prob. 13REAECh. 5 - Prob. 14REAECh. 5 - Prob. 15REAECh. 5 - Prob. 16REAECh. 5 - Prob. 17REAECh. 5 - Prob. 18REAECh. 5 - Prob. 19REAECh. 5 - Prob. 20REAECh. 5 - Prob. 21REAECh. 5 - Prob. 22REAECh. 5 - Prob. 23REAECh. 5 - Prob. 24REAECh. 5 - Prob. 25REAECh. 5 - Prob. 26REAECh. 5 - Prob. 27REAECh. 5 - Prob. 28REAECh. 5 - Prob. 29REAECh. 5 - Prob. 30REAECh. 5 - Prob. 31REAECh. 5 - Prob. 32REAECh. 5 - Prob. 33REAECh. 5 - Prob. 1TCh. 5 - Prob. 2TCh. 5 - Prob. 3TCh. 5 - Prob. 4TCh. 5 - Prob. 5TCh. 5 - Prob. 6TCh. 5 - Prob. 7TCh. 5 - Prob. 8TCh. 5 - Prob. 9TCh. 5 - Prob. 10TCh. 5 - Prob. 11TCh. 5 - Prob. 12TCh. 5 - Prob. 13TCh. 5 - Prob. 14TCh. 5 - Prob. 15TCh. 5 - Prob. 16TCh. 5 - Prob. 17TCh. 5 - Prob. 18TCh. 5 - Prob. 19TCh. 5 - Prob. 20TCh. 5 - Prob. 21TCh. 5 - Prob. 22TCh. 5 - Prob. 23TCh. 5 - Prob. 24TCh. 5 - Prob. 25TCh. 5 - Prob. 26TCh. 5 - Prob. 1PCh. 5 - Prob. 2PCh. 5 - Prob. 1TPCh. 5 - Prob. 2TPCh. 5 - Prob. 3TPCh. 5 - Prob. 4TPCh. 5 - Prob. 5TPCh. 5 - Prob. 6TPCh. 5 - Prob. 7TPCh. 5 - Prob. 8TPCh. 5 - Prob. 9TPCh. 5 - Prob. 10TPCh. 5 - Prob. 11TPCh. 5 - Prob. 12TPCh. 5 - Prob. 13TPCh. 5 - Prob. 14TPCh. 5 - Prob. 15TPCh. 5 - Prob. 16TPCh. 5 - Prob. 17TP
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