High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
15th Edition
ISBN: 9780133281163
Author: Prentice Hall
Publisher: Prentice Hall
Expert Solution & Answer
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Chapter 8.4, Problem 54PPSE
Solution

To find: The vertical asymptotes and holes of the graph of the rational function y=x3x3 .

The vertical asymptote is none and the hole is x=3 of the rational function.

Given:

The rational function is y=x3x3 .

Concept:

a Vertical asymptotes of a rational function: The vertical asymptotes of a rational function can be evaluated by reducing the rational function first and equate the denominator equal to zero. If the denominator is already in the reduced form, then simply equate it to zero to find the vertical asymptotes of the function.

b Holes of a rational function: The holes of a rational function can be evaluated by reducing the rational function first and look for common factors in numerator and denominator and equate the common term in numerator and denominator equal to zero to get the holes of the rational function. And, if the rational function is already in reduced form, then there are no holes in the rational function.

Calculation:

The rational function y=x3x3 and the reduce form of rational function is written as y=1 by cancelling the common x3 term in numerator and denominator. Now the reduced form of the rational function is y=1 . Therefore, using the clause a the rational function has no vertical asymptote.

is in reduced form because it has no common factors in numerator and denominator. Therefore, using the clause a , the vertical asymptote of the function is evaluated as:

  y=x3x3 ....Given ....1y=1 ....Reduced form1=0 ....Set denominator equal to zero, which is not possibleSo, no vertical asymptote.

The vertical asymptote is none.

From 1 , the rational function is y=x3x3 where common factor is x3 . Therefore, using the clause b equate x3 equal to zero to get the holes of the rational function.

  x3=0 ....Equate common term equal to 0x=3 .... which is the holeof rational funciton

The hole of the rational function is x=3 .

Conclusion:

The vertical asymptote is none and the hole is x=3 of the rational function.

Chapter 8 Solutions

High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11

Ch. 8.1 - Prob. 11PPSECh. 8.1 - Prob. 12PPSECh. 8.1 - Prob. 13PPSECh. 8.1 - Prob. 14PPSECh. 8.1 - Prob. 15PPSECh. 8.1 - Prob. 16PPSECh. 8.1 - Prob. 17PPSECh. 8.1 - Prob. 18PPSECh. 8.1 - Prob. 19PPSECh. 8.1 - Prob. 20PPSECh. 8.1 - Prob. 21PPSECh. 8.1 - Prob. 22PPSECh. 8.1 - Prob. 23PPSECh. 8.1 - Prob. 24PPSECh. 8.1 - Prob. 25PPSECh. 8.1 - Prob. 26PPSECh. 8.1 - Prob. 27PPSECh. 8.1 - Prob. 28PPSECh. 8.1 - Prob. 29PPSECh. 8.1 - Prob. 30PPSECh. 8.1 - Prob. 31PPSECh. 8.1 - Prob. 32PPSECh. 8.1 - Prob. 33PPSECh. 8.1 - Prob. 34PPSECh. 8.1 - Prob. 35PPSECh. 8.1 - Prob. 36PPSECh. 8.1 - Prob. 37PPSECh. 8.1 - Prob. 38PPSECh. 8.1 - Prob. 39PPSECh. 8.1 - Prob. 40PPSECh. 8.1 - Prob. 41PPSECh. 8.1 - Prob. 42PPSECh. 8.1 - Prob. 43PPSECh. 8.1 - Prob. 44PPSECh. 8.1 - Prob. 45PPSECh. 8.1 - Prob. 46PPSECh. 8.1 - Prob. 47PPSECh. 8.1 - Prob. 48PPSECh. 8.1 - Prob. 49PPSECh. 8.1 - Prob. 50PPSECh. 8.1 - Prob. 51PPSECh. 8.1 - Prob. 52PPSECh. 8.1 - Prob. 53PPSECh. 8.1 - Prob. 54PPSECh. 8.1 - Prob. 55PPSECh. 8.1 - Prob. 56PPSECh. 8.1 - Prob. 57PPSECh. 8.1 - Prob. 58PPSECh. 8.1 - Prob. 59PPSECh. 8.1 - Prob. 60PPSECh. 8.2 - Prob. 1ECh. 8.2 - Prob. 2ECh. 8.2 - Prob. 3ECh. 8.2 - Prob. 4ECh. 8.2 - Prob. 5ECh. 8.2 - Prob. 6ECh. 8.2 - Prob. 7ECh. 8.2 - Prob. 8ECh. 8.2 - Prob. 9ECh. 8.2 - Prob. 10ECh. 8.2 - Prob. 11ECh. 8.2 - Prob. 1LCCh. 8.2 - Prob. 2LCCh. 8.2 - Prob. 3LCCh. 8.2 - Prob. 4LCCh. 8.2 - Prob. 5LCCh. 8.2 - Prob. 6LCCh. 8.2 - Prob. 7LCCh. 8.2 - Prob. 8PPSECh. 8.2 - Prob. 9PPSECh. 8.2 - Prob. 10PPSECh. 8.2 - Prob. 11PPSECh. 8.2 - Prob. 12PPSECh. 8.2 - Prob. 13PPSECh. 8.2 - Prob. 14PPSECh. 8.2 - Prob. 15PPSECh. 8.2 - Prob. 16PPSECh. 8.2 - Prob. 17PPSECh. 8.2 - Prob. 18PPSECh. 8.2 - Prob. 19PPSECh. 8.2 - Prob. 20PPSECh. 8.2 - Prob. 21PPSECh. 8.2 - Prob. 22PPSECh. 8.2 - Prob. 23PPSECh. 8.2 - Prob. 24PPSECh. 8.2 - Prob. 25PPSECh. 8.2 - Prob. 26PPSECh. 8.2 - Prob. 27PPSECh. 8.2 - Prob. 28PPSECh. 8.2 - Prob. 29PPSECh. 8.2 - Prob. 30PPSECh. 8.2 - Prob. 31PPSECh. 8.2 - Prob. 32PPSECh. 8.2 - Prob. 33PPSECh. 8.2 - Prob. 34PPSECh. 8.2 - Prob. 35PPSECh. 8.2 - Prob. 36PPSECh. 8.2 - Prob. 37PPSECh. 8.2 - Prob. 38PPSECh. 8.2 - Prob. 39PPSECh. 8.2 - Prob. 40PPSECh. 8.2 - Prob. 41PPSECh. 8.2 - Prob. 42PPSECh. 8.2 - Prob. 43PPSECh. 8.2 - Prob. 44PPSECh. 8.2 - Prob. 45PPSECh. 8.2 - Prob. 46PPSECh. 8.2 - Prob. 47PPSECh. 8.2 - Prob. 48PPSECh. 8.2 - Prob. 49PPSECh. 8.2 - Prob. 50PPSECh. 8.2 - Prob. 51PPSECh. 8.2 - Prob. 52PPSECh. 8.2 - Prob. 53PPSECh. 8.3 - Prob. 1LCCh. 8.3 - Prob. 2LCCh. 8.3 - Prob. 3LCCh. 8.3 - Prob. 4LCCh. 8.3 - Prob. 5LCCh. 8.3 - Prob. 6LCCh. 8.3 - Prob. 7LCCh. 8.3 - Prob. 8LCCh. 8.3 - Prob. 9LCCh. 8.3 - Prob. 10LCCh. 8.3 - Prob. 11LCCh. 8.3 - Prob. 12LCCh. 8.3 - Prob. 13PPSECh. 8.3 - Prob. 14PPSECh. 8.3 - Prob. 15PPSECh. 8.3 - Prob. 16PPSECh. 8.3 - Prob. 17PPSECh. 8.3 - Prob. 18PPSECh. 8.3 - Prob. 19PPSECh. 8.3 - Prob. 20PPSECh. 8.3 - Prob. 21PPSECh. 8.3 - Prob. 22PPSECh. 8.3 - Prob. 23PPSECh. 8.3 - Prob. 24PPSECh. 8.3 - Prob. 25PPSECh. 8.3 - Prob. 26PPSECh. 8.3 - Prob. 27PPSECh. 8.3 - Prob. 28PPSECh. 8.3 - Prob. 29PPSECh. 8.3 - Prob. 30PPSECh. 8.3 - Prob. 31PPSECh. 8.3 - Prob. 32PPSECh. 8.3 - Prob. 33PPSECh. 8.3 - Prob. 34PPSECh. 8.3 - Prob. 35PPSECh. 8.3 - Prob. 36PPSECh. 8.3 - Prob. 37PPSECh. 8.3 - Prob. 38PPSECh. 8.3 - Prob. 39PPSECh. 8.3 - Prob. 40PPSECh. 8.3 - Prob. 41PPSECh. 8.3 - Prob. 42PPSECh. 8.3 - Prob. 43PPSECh. 8.3 - Prob. 44PPSECh. 8.3 - Prob. 45PPSECh. 8.3 - Prob. 46PPSECh. 8.3 - Prob. 47PPSECh. 8.3 - Prob. 48PPSECh. 8.3 - Prob. 49PPSECh. 8.3 - Prob. 50PPSECh. 8.3 - Prob. 51PPSECh. 8.3 - Prob. 52PPSECh. 8.3 - Prob. 53PPSECh. 8.3 - Prob. 54PPSECh. 8.3 - Prob. 55PPSECh. 8.3 - Prob. 56PPSECh. 8.3 - Prob. 57PPSECh. 8.3 - Prob. 58PPSECh. 8.3 - Prob. 59PPSECh. 8.3 - Prob. 60PPSECh. 8.3 - Prob. 61PPSECh. 8.3 - Prob. 62PPSECh. 8.3 - Prob. 63PPSECh. 8.3 - Prob. 64PPSECh. 8.3 - Prob. 65PPSECh. 8.3 - Prob. 66PPSECh. 8.3 - Prob. 67PPSECh. 8.3 - Prob. 68PPSECh. 8.3 - Prob. 69PPSECh. 8.3 - Prob. 70PPSECh. 8.3 - Prob. 71PPSECh. 8.3 - Prob. 72PPSECh. 8.3 - Prob. 73PPSECh. 8.3 - Prob. 74PPSECh. 8.3 - Prob. 75PPSECh. 8.3 - Prob. 76PPSECh. 8.3 - Prob. 1ECh. 8.3 - Prob. 2ECh. 8.3 - Prob. 3ECh. 8.3 - Prob. 4ECh. 8.3 - Prob. 5ECh. 8.3 - Prob. 6ECh. 8.3 - Prob. 7ECh. 8.3 - Prob. 8ECh. 8.3 - Prob. 9ECh. 8.3 - Prob. 10ECh. 8.3 - Prob. 11ECh. 8.3 - Prob. 12ECh. 8.4 - Prob. 1LCCh. 8.4 - Prob. 2LCCh. 8.4 - Prob. 3LCCh. 8.4 - Prob. 4LCCh. 8.4 - Prob. 5LCCh. 8.4 - Prob. 6LCCh. 8.4 - Prob. 7LCCh. 8.4 - Prob. 8PPSECh. 8.4 - Prob. 9PPSECh. 8.4 - Prob. 10PPSECh. 8.4 - Prob. 11PPSECh. 8.4 - Prob. 12PPSECh. 8.4 - Prob. 13PPSECh. 8.4 - Prob. 14PPSECh. 8.4 - Prob. 15PPSECh. 8.4 - Prob. 16PPSECh. 8.4 - Prob. 17PPSECh. 8.4 - Prob. 18PPSECh. 8.4 - Prob. 19PPSECh. 8.4 - Prob. 20PPSECh. 8.4 - Prob. 21PPSECh. 8.4 - Prob. 22PPSECh. 8.4 - Prob. 23PPSECh. 8.4 - Prob. 24PPSECh. 8.4 - Prob. 25PPSECh. 8.4 - Prob. 26PPSECh. 8.4 - Prob. 27PPSECh. 8.4 - Prob. 28PPSECh. 8.4 - Prob. 29PPSECh. 8.4 - Prob. 30PPSECh. 8.4 - Prob. 31PPSECh. 8.4 - Prob. 32PPSECh. 8.4 - Prob. 33PPSECh. 8.4 - Prob. 34PPSECh. 8.4 - Prob. 35PPSECh. 8.4 - Prob. 36PPSECh. 8.4 - Prob. 37PPSECh. 8.4 - Prob. 38PPSECh. 8.4 - Prob. 39PPSECh. 8.4 - Prob. 40PPSECh. 8.4 - Prob. 41PPSECh. 8.4 - Prob. 42PPSECh. 8.4 - Prob. 43PPSECh. 8.4 - Prob. 44PPSECh. 8.4 - Prob. 45PPSECh. 8.4 - Prob. 46PPSECh. 8.4 - Prob. 47PPSECh. 8.4 - Prob. 48PPSECh. 8.4 - Prob. 49PPSECh. 8.4 - Prob. 50PPSECh. 8.4 - Prob. 51PPSECh. 8.4 - Prob. 52PPSECh. 8.4 - Prob. 53PPSECh. 8.4 - Prob. 54PPSECh. 8.4 - Prob. 55PPSECh. 8.4 - Prob. 56PPSECh. 8.4 - Prob. 57PPSECh. 8.4 - Prob. 58PPSECh. 8.4 - Prob. 59PPSECh. 8.4 - Prob. 60PPSECh. 8.4 - Prob. 61PPSECh. 8.4 - Prob. 62PPSECh. 8.4 - Prob. 63PPSECh. 8.4 - Prob. 64PPSECh. 8.4 - Prob. 65PPSECh. 8.4 - Prob. 66PPSECh. 8.4 - Prob. 67PPSECh. 8.5 - Prob. 1LCCh. 8.5 - Prob. 2LCCh. 8.5 - Prob. 3LCCh. 8.5 - Prob. 4LCCh. 8.5 - Prob. 5LCCh. 8.5 - Prob. 6LCCh. 8.5 - Prob. 7PPSECh. 8.5 - Prob. 8PPSECh. 8.5 - Prob. 9PPSECh. 8.5 - Prob. 10PPSECh. 8.5 - Prob. 11PPSECh. 8.5 - Prob. 12PPSECh. 8.5 - Prob. 13PPSECh. 8.5 - Prob. 14PPSECh. 8.5 - Prob. 15PPSECh. 8.5 - Prob. 16PPSECh. 8.5 - Prob. 17PPSECh. 8.5 - Prob. 18PPSECh. 8.5 - Prob. 19PPSECh. 8.5 - Prob. 20PPSECh. 8.5 - Prob. 21PPSECh. 8.5 - Prob. 22PPSECh. 8.5 - Prob. 23PPSECh. 8.5 - Prob. 24PPSECh. 8.5 - Prob. 25PPSECh. 8.5 - Prob. 26PPSECh. 8.5 - Prob. 27PPSECh. 8.5 - Prob. 28PPSECh. 8.5 - Prob. 29PPSECh. 8.5 - Prob. 30PPSECh. 8.5 - Prob. 31PPSECh. 8.5 - Prob. 32PPSECh. 8.5 - Prob. 33PPSECh. 8.5 - Prob. 34PPSECh. 8.5 - Prob. 35PPSECh. 8.5 - Prob. 36PPSECh. 8.5 - Prob. 37PPSECh. 8.5 - Prob. 38PPSECh. 8.5 - Prob. 39PPSECh. 8.5 - Prob. 40PPSECh. 8.5 - Prob. 41PPSECh. 8.5 - Prob. 42PPSECh. 8.5 - Prob. 43PPSECh. 8.5 - Prob. 44PPSECh. 8.5 - Prob. 45PPSECh. 8.5 - Prob. 46PPSECh. 8.5 - Prob. 47PPSECh. 8.5 - Prob. 48PPSECh. 8.5 - Prob. 49PPSECh. 8.5 - Prob. 50PPSECh. 8.5 - Prob. 51PPSECh. 8.5 - Prob. 52PPSECh. 8.6 - Prob. 1LCCh. 8.6 - Prob. 2LCCh. 8.6 - Prob. 3LCCh. 8.6 - Prob. 4LCCh. 8.6 - Prob. 5LCCh. 8.6 - Prob. 6LCCh. 8.6 - Prob. 7LCCh. 8.6 - Prob. 8PPSECh. 8.6 - Prob. 9PPSECh. 8.6 - Prob. 10PPSECh. 8.6 - Prob. 11PPSECh. 8.6 - Prob. 12PPSECh. 8.6 - Prob. 13PPSECh. 8.6 - Prob. 14PPSECh. 8.6 - Prob. 15PPSECh. 8.6 - Prob. 16PPSECh. 8.6 - Prob. 17PPSECh. 8.6 - Prob. 18PPSECh. 8.6 - Prob. 19PPSECh. 8.6 - Prob. 20PPSECh. 8.6 - Prob. 21PPSECh. 8.6 - Prob. 22PPSECh. 8.6 - Prob. 23PPSECh. 8.6 - Prob. 24PPSECh. 8.6 - Prob. 25PPSECh. 8.6 - Prob. 26PPSECh. 8.6 - Prob. 27PPSECh. 8.6 - Prob. 28PPSECh. 8.6 - Prob. 29PPSECh. 8.6 - Prob. 30PPSECh. 8.6 - Prob. 31PPSECh. 8.6 - Prob. 32PPSECh. 8.6 - Prob. 33PPSECh. 8.6 - Prob. 34PPSECh. 8.6 - Prob. 35PPSECh. 8.6 - Prob. 36PPSECh. 8.6 - Prob. 37PPSECh. 8.6 - Prob. 38PPSECh. 8.6 - Prob. 39PPSECh. 8.6 - Prob. 40PPSECh. 8.6 - Prob. 41PPSECh. 8.6 - Prob. 42PPSECh. 8.6 - Prob. 43PPSECh. 8.6 - Prob. 44PPSECh. 8.6 - Prob. 45PPSECh. 8.6 - Prob. 46PPSECh. 8.6 - Prob. 47PPSECh. 8.6 - Prob. 48PPSECh. 8.6 - Prob. 49PPSECh. 8.6 - Prob. 50PPSECh. 8.6 - Prob. 51PPSECh. 8.6 - Prob. 52PPSECh. 8.6 - Prob. 53PPSECh. 8.6 - Prob. 54PPSECh. 8.6 - Prob. 55PPSECh. 8.6 - Prob. 56PPSECh. 8.6 - Prob. 57PPSECh. 8.6 - Prob. 58PPSECh. 8.6 - Prob. 59PPSECh. 8.6 - Prob. 60PPSECh. 8.6 - Prob. 1ACh. 8.6 - Prob. 2ACh. 8.6 - Prob. 3ACh. 8.6 - Prob. 4ACh. 8.6 - Prob. 5ACh. 8.6 - Prob. 6ACh. 8.6 - Prob. 7ACh. 8.6 - Prob. 8ECh. 8.6 - Prob. 9ECh. 8.6 - Prob. 10ECh. 8.6 - Prob. 11ECh. 8.6 - Prob. 12ECh. 8.6 - Prob. 1.1ACh. 8.6 - Prob. 1.2ACh. 8.6 - Prob. 1.3ACh. 8.6 - Prob. 1.4ACh. 8.6 - Prob. 1.5ACh. 8.6 - Prob. 1.6ACh. 8.6 - Prob. 1.7ACh. 8.6 - Prob. 1.8ACh. 8.6 - Prob. 1.9ACh. 8.6 - Prob. 1.10ACh. 8.6 - Prob. 1.11ACh. 8.6 - Prob. 1.12ECh. 8.6 - Prob. 1.13ECh. 8.6 - Prob. 1.14ECh. 8.6 - Prob. 1.15ECh. 8.6 - Prob. 1.16ECh. 8.6 - Prob. 1.17ECh. 8.6 - Prob. 1.18ECh. 8.6 - Prob. 1.19ECh. 8 - Prob. 1GRCh. 8 - Prob. 2GRCh. 8 - Prob. 3GRCh. 8 - Prob. 4GRCh. 8 - Prob. 5GRCh. 8 - Prob. 6GRCh. 8 - Prob. 7GRCh. 8 - Prob. 8GRCh. 8 - Prob. 9GRCh. 8 - Prob. 10GRCh. 8 - Prob. 11GRCh. 8 - Prob. 12GRCh. 8 - Prob. 13GRCh. 8 - Prob. 14GRCh. 8 - Prob. 15GRCh. 8 - Prob. 16GRCh. 8 - Prob. 17GRCh. 8 - Prob. 18GRCh. 8 - Prob. 1MCQCh. 8 - Prob. 2MCQCh. 8 - Prob. 3MCQCh. 8 - Prob. 4MCQCh. 8 - Prob. 5MCQCh. 8 - Prob. 6MCQCh. 8 - Prob. 7MCQCh. 8 - Prob. 8MCQCh. 8 - Prob. 9MCQCh. 8 - Prob. 10MCQCh. 8 - Prob. 11MCQCh. 8 - Prob. 12MCQCh. 8 - Prob. 13MCQCh. 8 - Prob. 14MCQCh. 8 - Prob. 15MCQCh. 8 - Prob. 16MCQCh. 8 - Prob. 17MCQCh. 8 - Prob. 18MCQCh. 8 - Prob. 19MCQCh. 8 - Prob. 20MCQCh. 8 - Prob. 21MCQCh. 8 - Prob. 22MCQCh. 8 - Prob. 23MCQCh. 8 - Prob. 24MCQCh. 8 - Prob. 25MCQCh. 8 - Prob. 26MCQCh. 8 - Prob. 27MCQCh. 8 - Prob. 28MCQCh. 8 - Prob. 1CVCh. 8 - Prob. 2CVCh. 8 - Prob. 3CVCh. 8 - Prob. 4CVCh. 8 - Prob. 5CVCh. 8 - Prob. 6ECh. 8 - Prob. 7ECh. 8 - Prob. 8ECh. 8 - Prob. 9ECh. 8 - Prob. 10ECh. 8 - Prob. 11ECh. 8 - Prob. 12ECh. 8 - Prob. 13ECh. 8 - Prob. 14ECh. 8 - Prob. 15ECh. 8 - Prob. 16ECh. 8 - Prob. 17ECh. 8 - Prob. 18ECh. 8 - Prob. 19ECh. 8 - Prob. 20ECh. 8 - Prob. 21ECh. 8 - Prob. 22ECh. 8 - Prob. 23ECh. 8 - Prob. 24ECh. 8 - Prob. 25ECh. 8 - Prob. 26ECh. 8 - Prob. 27ECh. 8 - Prob. 28ECh. 8 - Prob. 29ECh. 8 - Prob. 30ECh. 8 - Prob. 31ECh. 8 - Prob. 32ECh. 8 - Prob. 33ECh. 8 - Prob. 34ECh. 8 - Prob. 1CTCh. 8 - Prob. 2CTCh. 8 - Prob. 3CTCh. 8 - Prob. 4CTCh. 8 - Prob. 5CTCh. 8 - Prob. 6CTCh. 8 - Prob. 7CTCh. 8 - Prob. 8CTCh. 8 - Prob. 9CTCh. 8 - Prob. 10CTCh. 8 - Prob. 11CTCh. 8 - Prob. 12CTCh. 8 - Prob. 13CTCh. 8 - Prob. 14CTCh. 8 - Prob. 15CTCh. 8 - Prob. 16CTCh. 8 - Prob. 17CTCh. 8 - Prob. 18CTCh. 8 - Prob. 19CTCh. 8 - Prob. 20CTCh. 8 - Prob. 21CTCh. 8 - Prob. 22CTCh. 8 - Prob. 23CTCh. 8 - Prob. 24CTCh. 8 - Prob. 25CTCh. 8 - Prob. 26CTCh. 8 - Prob. 27CTCh. 8 - Prob. 28CTCh. 8 - Prob. 29CTCh. 8 - Prob. 30CTCh. 8 - Prob. 31CTCh. 8 - Prob. 1CCSRCh. 8 - Prob. 2CCSRCh. 8 - Prob. 3CCSRCh. 8 - Prob. 4CCSRCh. 8 - Prob. 5CCSRCh. 8 - Prob. 6CCSRCh. 8 - Prob. 7CCSRCh. 8 - Prob. 8CCSRCh. 8 - Prob. 9CCSRCh. 8 - Prob. 10CCSRCh. 8 - Prob. 11CCSRCh. 8 - Prob. 12CCSRCh. 8 - Prob. 13CCSRCh. 8 - Prob. 14CCSRCh. 8 - Prob. 15CCSRCh. 8 - Prob. 16CCSRCh. 8 - Prob. 17CCSRCh. 8 - Prob. 18CCSRCh. 8 - 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