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 5.1, Problem 32PPSE
Solution

To Describe: The shape of the graph of each cubic function including end behavior, turning points, and increasing/decreasing intervals.

The graph's end behavior falls to the left and rises to the right.

There are 2 turning points: x=13,−13

Increasing on: −∞,−13,13,∞

Decreasing on: −13,13

Given:

  y=3x3−x−3

Explanation:

Given the function y=3x3−x−3

To create a table of values, substitute values to the equation.

Substitute x=−2 in y=3x3−x−3 :

  y=3−23−−2−3=3−8+2−3=−24+2−3=−22−3=−25

Substitute x=−1 in y=3x3−x−3 :

  y=3−13−−1−3=3−1+1−3=−3+1−3=−5

Substitute x=0 in y=3x3−x−3 :

  y=303−0−3=−3

Substitute x=1 in y=3x3−x−3 :

  y=313−1−3=31−1−3=3−1−3=−1

Substitute x=2 in y=3x3−x−3 :

  y=323−2−3=38−2−3=24−2−3=24−5=19

    xy
    −2−25
    −1−5
    0−3
    1−1
    219

Graph of the function is as:

  High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11, Chapter 5.1, Problem 32PPSE

Find the end behaviour of y=3x3−x−3 :

The leading coefficient in a polynomial is the coefficient of the leading term which is 3 .

Since the degree is odd, the ends of the function will point in the opposite directions.

Since the leading coefficient is positive, the graph rises to the right.

The graph's end behaviour is falls to the left and rises to the right.

To find the turning points, set y′x=0

  y=3x3−x−3y′=9x2−1

Set the equation to 0 :

  9x2−1=09x2=1x2=19x=±13x=+13,−13

Thus, there are 2 turning points.

Determine the interval of increasing/decreasing:

By using the graph, the graph is

Increasing on: −∞,−13,13,∞

Decreasing on: −13,13

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Chapter 5.1, Problem 31PPSE
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Chapter 5.1, Problem 33PPSE

Chapter 5 Solutions

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

Ch. 5.1 - Prob. 1LCCh. 5.1 - Prob. 2LCCh. 5.1 - Prob. 3LCCh. 5.1 - Prob. 4LCCh. 5.1 - Prob. 5LCCh. 5.1 - Prob. 6LCCh. 5.1 - Prob. 7LCCh. 5.1 - Prob. 8PPSECh. 5.1 - Prob. 9PPSECh. 5.1 - Prob. 10PPSE
Ch. 5.1 - Prob. 11PPSECh. 5.1 - Prob. 12PPSECh. 5.1 - Prob. 13PPSECh. 5.1 - Prob. 14PPSECh. 5.1 - Prob. 15PPSECh. 5.1 - Prob. 16PPSECh. 5.1 - Prob. 17PPSECh. 5.1 - Prob. 18PPSECh. 5.1 - Prob. 19PPSECh. 5.1 - Prob. 20PPSECh. 5.1 - Prob. 21PPSECh. 5.1 - Prob. 22PPSECh. 5.1 - Prob. 23PPSECh. 5.1 - Prob. 24PPSECh. 5.1 - Prob. 25PPSECh. 5.1 - Prob. 26PPSECh. 5.1 - Prob. 27PPSECh. 5.1 - Prob. 28PPSECh. 5.1 - Prob. 29PPSECh. 5.1 - Prob. 30PPSECh. 5.1 - Prob. 31PPSECh. 5.1 - Prob. 32PPSECh. 5.1 - Prob. 33PPSECh. 5.1 - Prob. 34PPSECh. 5.1 - Prob. 35PPSECh. 5.1 - Prob. 36PPSECh. 5.1 - Prob. 37PPSECh. 5.1 - Prob. 38PPSECh. 5.1 - Prob. 39PPSECh. 5.1 - Prob. 40PPSECh. 5.1 - Prob. 41PPSECh. 5.1 - Prob. 42PPSECh. 5.1 - Prob. 43PPSECh. 5.1 - Prob. 44PPSECh. 5.1 - Prob. 45PPSECh. 5.1 - Prob. 46PPSECh. 5.1 - Prob. 47PPSECh. 5.1 - Prob. 48PPSECh. 5.1 - Prob. 49PPSECh. 5.1 - Prob. 50PPSECh. 5.1 - Prob. 51PPSECh. 5.1 - Prob. 52PPSECh. 5.1 - Prob. 53PPSECh. 5.1 - Prob. 54PPSECh. 5.1 - Prob. 55PPSECh. 5.1 - Prob. 56PPSECh. 5.1 - Prob. 57PPSECh. 5.2 - Prob. 1LCCh. 5.2 - Prob. 2LCCh. 5.2 - Prob. 3LCCh. 5.2 - Prob. 4LCCh. 5.2 - Prob. 5LCCh. 5.2 - Prob. 6LCCh. 5.2 - Prob. 7PPSECh. 5.2 - Prob. 8PPSECh. 5.2 - Prob. 9PPSECh. 5.2 - Prob. 10PPSECh. 5.2 - Prob. 11PPSECh. 5.2 - Prob. 12PPSECh. 5.2 - Prob. 13PPSECh. 5.2 - Prob. 14PPSECh. 5.2 - Prob. 15PPSECh. 5.2 - Prob. 16PPSECh. 5.2 - Prob. 17PPSECh. 5.2 - Prob. 18PPSECh. 5.2 - Prob. 19PPSECh. 5.2 - Prob. 20PPSECh. 5.2 - Prob. 21PPSECh. 5.2 - Prob. 22PPSECh. 5.2 - Prob. 23PPSECh. 5.2 - Prob. 24PPSECh. 5.2 - Prob. 25PPSECh. 5.2 - Prob. 26PPSECh. 5.2 - Prob. 27PPSECh. 5.2 - Prob. 28PPSECh. 5.2 - Prob. 29PPSECh. 5.2 - Prob. 30PPSECh. 5.2 - Prob. 31PPSECh. 5.2 - Prob. 32PPSECh. 5.2 - Prob. 33PPSECh. 5.2 - Prob. 34PPSECh. 5.2 - Prob. 35PPSECh. 5.2 - Prob. 36PPSECh. 5.2 - Prob. 37PPSECh. 5.2 - Prob. 38PPSECh. 5.2 - Prob. 39PPSECh. 5.2 - Prob. 40PPSECh. 5.2 - Prob. 41PPSECh. 5.2 - Prob. 42PPSECh. 5.2 - Prob. 43PPSECh. 5.2 - Prob. 44PPSECh. 5.2 - Prob. 45PPSECh. 5.2 - 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Prob. 20PPSECh. 5.5 - Prob. 21PPSECh. 5.5 - Prob. 22PPSECh. 5.5 - Prob. 23PPSECh. 5.5 - Prob. 24PPSECh. 5.5 - Prob. 25PPSECh. 5.5 - Prob. 26PPSECh. 5.5 - Prob. 27PPSECh. 5.5 - Prob. 28PPSECh. 5.5 - Prob. 29PPSECh. 5.5 - Prob. 30PPSECh. 5.5 - Prob. 31PPSECh. 5.5 - Prob. 32PPSECh. 5.5 - Prob. 33PPSECh. 5.5 - Prob. 34PPSECh. 5.5 - Prob. 35PPSECh. 5.5 - Prob. 36PPSECh. 5.5 - Prob. 37PPSECh. 5.5 - Prob. 38PPSECh. 5.5 - Prob. 39PPSECh. 5.5 - Prob. 40PPSECh. 5.5 - Prob. 41PPSECh. 5.5 - Prob. 42PPSECh. 5.5 - Prob. 43PPSECh. 5.5 - Prob. 44PPSECh. 5.5 - Prob. 45PPSECh. 5.5 - Prob. 46PPSECh. 5.5 - Prob. 47PPSECh. 5.5 - Prob. 48PPSECh. 5.5 - Prob. 49PPSECh. 5.5 - Prob. 1ECh. 5.5 - Prob. 2ECh. 5.5 - Prob. 3ECh. 5.5 - Prob. 4ECh. 5.5 - Prob. 5ECh. 5.6 - Prob. 1LCCh. 5.6 - Prob. 2LCCh. 5.6 - Prob. 3LCCh. 5.6 - Prob. 4LCCh. 5.6 - Prob. 5LCCh. 5.6 - Prob. 6LCCh. 5.6 - Prob. 7LCCh. 5.6 - Prob. 8PPSECh. 5.6 - Prob. 9PPSECh. 5.6 - Prob. 10PPSECh. 5.6 - Prob. 11PPSECh. 5.6 - Prob. 12PPSECh. 5.6 - Prob. 13PPSECh. 5.6 - Prob. 14PPSECh. 5.6 - Prob. 15PPSECh. 5.6 - Prob. 16PPSECh. 5.6 - Prob. 17PPSECh. 5.6 - Prob. 18PPSECh. 5.6 - Prob. 19PPSECh. 5.6 - Prob. 20PPSECh. 5.6 - Prob. 21PPSECh. 5.6 - Prob. 22PPSECh. 5.6 - Prob. 23PPSECh. 5.6 - Prob. 24PPSECh. 5.6 - Prob. 25PPSECh. 5.6 - Prob. 26PPSECh. 5.6 - Prob. 27PPSECh. 5.6 - Prob. 28PPSECh. 5.6 - Prob. 29PPSECh. 5.6 - Prob. 30PPSECh. 5.6 - Prob. 31PPSECh. 5.6 - Prob. 32PPSECh. 5.6 - Prob. 33PPSECh. 5.6 - Prob. 34PPSECh. 5.6 - Prob. 35PPSECh. 5.6 - Prob. 36PPSECh. 5.6 - Prob. 37PPSECh. 5.6 - Prob. 38PPSECh. 5.6 - Prob. 39PPSECh. 5.6 - Prob. 40PPSECh. 5.6 - Prob. 41PPSECh. 5.6 - Prob. 42PPSECh. 5.6 - Prob. 43PPSECh. 5.6 - Prob. 44PPSECh. 5.6 - Prob. 45PPSECh. 5.6 - Prob. 46PPSECh. 5.6 - Prob. 47PPSECh. 5.6 - Prob. 48PPSECh. 5.6 - Prob. 49PPSECh. 5.6 - Prob. 50PPSECh. 5.6 - Prob. 51PPSECh. 5.6 - Prob. 52PPSECh. 5.6 - Prob. 53PPSECh. 5.6 - Prob. 54PPSECh. 5.6 - Prob. 55PPSECh. 5.6 - Prob. 56PPSECh. 5.6 - Prob. 57PPSECh. 5.6 - Prob. 58PPSECh. 5.6 - Prob. 59PPSECh. 5.6 - Prob. 60PPSECh. 5.6 - Prob. 61PPSECh. 5.6 - Prob. 62PPSECh. 5.6 - Prob. 63PPSECh. 5.6 - Prob. 64PPSECh. 5.6 - Prob. 65PPSECh. 5.6 - Prob. 1ECh. 5.6 - Prob. 2ECh. 5.6 - Prob. 3ECh. 5.6 - Prob. 4ECh. 5.6 - Prob. 5ECh. 5.6 - Prob. 6ECh. 5.7 - Prob. 1LCCh. 5.7 - Prob. 2LCCh. 5.7 - Prob. 3LCCh. 5.7 - Prob. 4LCCh. 5.7 - Prob. 5LCCh. 5.7 - Prob. 6LCCh. 5.7 - Prob. 7LCCh. 5.7 - Prob. 8PPSECh. 5.7 - Prob. 9PPSECh. 5.7 - Prob. 10PPSECh. 5.7 - Prob. 11PPSECh. 5.7 - Prob. 12PPSECh. 5.7 - Prob. 13PPSECh. 5.7 - Prob. 14PPSECh. 5.7 - Prob. 15PPSECh. 5.7 - Prob. 16PPSECh. 5.7 - Prob. 17PPSECh. 5.7 - Prob. 18PPSECh. 5.7 - Prob. 19PPSECh. 5.7 - Prob. 20PPSECh. 5.7 - Prob. 21PPSECh. 5.7 - Prob. 22PPSECh. 5.7 - Prob. 23PPSECh. 5.7 - Prob. 24PPSECh. 5.7 - Prob. 25PPSECh. 5.7 - Prob. 26PPSECh. 5.7 - Prob. 27PPSECh. 5.7 - Prob. 28PPSECh. 5.7 - Prob. 29PPSECh. 5.7 - Prob. 30PPSECh. 5.7 - Prob. 31PPSECh. 5.7 - Prob. 32PPSECh. 5.7 - Prob. 33PPSECh. 5.7 - Prob. 34PPSECh. 5.7 - Prob. 35PPSECh. 5.7 - Prob. 36PPSECh. 5.7 - 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Prob. 16PPSECh. 5.8 - Prob. 17PPSECh. 5.8 - Prob. 18PPSECh. 5.8 - Prob. 19PPSECh. 5.8 - Prob. 20PPSECh. 5.8 - Prob. 21PPSECh. 5.8 - Prob. 22PPSECh. 5.8 - Prob. 23PPSECh. 5.8 - Prob. 24PPSECh. 5.8 - Prob. 25PPSECh. 5.8 - Prob. 26PPSECh. 5.8 - Prob. 27PPSECh. 5.8 - Prob. 28PPSECh. 5.8 - Prob. 29PPSECh. 5.8 - Prob. 30PPSECh. 5.8 - Prob. 31PPSECh. 5.8 - Prob. 32PPSECh. 5.8 - Prob. 33PPSECh. 5.8 - Prob. 34PPSECh. 5.8 - Prob. 35PPSECh. 5.8 - Prob. 36PPSECh. 5.8 - Prob. 37PPSECh. 5.8 - Prob. 38PPSECh. 5.8 - Prob. 39PPSECh. 5.8 - Prob. 40PPSECh. 5.8 - Prob. 41PPSECh. 5.8 - Prob. 42PPSECh. 5.8 - Prob. 43PPSECh. 5.8 - Prob. 44PPSECh. 5.8 - Prob. 45PPSECh. 5.8 - Prob. 46PPSECh. 5.8 - Prob. 47PPSECh. 5.8 - Prob. 48PPSECh. 5.8 - Prob. 49PPSECh. 5.8 - Prob. 50PPSECh. 5.8 - Prob. 51PPSECh. 5.8 - Prob. 52PPSECh. 5.8 - Prob. 53PPSECh. 5.8 - Prob. 54PPSECh. 5.8 - Prob. 55PPSECh. 5.8 - Prob. 56PPSECh. 5.8 - Prob. 57PPSECh. 5.8 - Prob. 58PPSECh. 5.9 - Prob. 1LCCh. 5.9 - Prob. 2LCCh. 5.9 - Prob. 3LCCh. 5.9 - 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Prob. 50PPSECh. 5.9 - Prob. 51PPSECh. 5.9 - Prob. 52PPSECh. 5.9 - Prob. 53PPSECh. 5.9 - Prob. 54PPSECh. 5.9 - Prob. 55PPSECh. 5.9 - Prob. 56PPSECh. 5 - Prob. 1GRCh. 5 - Prob. 2GRCh. 5 - Prob. 3GRCh. 5 - Prob. 4GRCh. 5 - Prob. 5GRCh. 5 - Prob. 6GRCh. 5 - Prob. 7GRCh. 5 - Prob. 8GRCh. 5 - Prob. 9GRCh. 5 - Prob. 10GRCh. 5 - Prob. 11GRCh. 5 - Prob. 12GRCh. 5 - Prob. 13GRCh. 5 - Prob. 14GRCh. 5 - Prob. 15GRCh. 5 - Prob. 16GRCh. 5 - Prob. 17GRCh. 5 - Prob. 18GRCh. 5 - Prob. 1MCQCh. 5 - Prob. 2MCQCh. 5 - Prob. 3MCQCh. 5 - Prob. 4MCQCh. 5 - Prob. 5MCQCh. 5 - Prob. 6MCQCh. 5 - Prob. 7MCQCh. 5 - Prob. 8MCQCh. 5 - Prob. 9MCQCh. 5 - Prob. 10MCQCh. 5 - Prob. 11MCQCh. 5 - Prob. 12MCQCh. 5 - Prob. 13MCQCh. 5 - Prob. 14MCQCh. 5 - Prob. 15MCQCh. 5 - Prob. 16MCQCh. 5 - Prob. 17MCQCh. 5 - Prob. 18MCQCh. 5 - Prob. 19MCQCh. 5 - Prob. 1CVCh. 5 - Prob. 2CVCh. 5 - Prob. 3CVCh. 5 - Prob. 4CVCh. 5 - Prob. 5ECh. 5 - Prob. 6ECh. 5 - Prob. 7ECh. 5 - Prob. 8ECh. 5 - Prob. 9ECh. 5 - Prob. 10ECh. 5 - Prob. 11ECh. 5 - Prob. 12ECh. 5 - Prob. 13ECh. 5 - Prob. 14ECh. 5 - Prob. 15ECh. 5 - Prob. 16ECh. 5 - Prob. 17ECh. 5 - Prob. 18ECh. 5 - Prob. 19ECh. 5 - Prob. 20ECh. 5 - Prob. 21ECh. 5 - Prob. 22ECh. 5 - Prob. 23ECh. 5 - Prob. 24ECh. 5 - Prob. 25ECh. 5 - Prob. 26ECh. 5 - Prob. 27ECh. 5 - Prob. 28ECh. 5 - Prob. 29ECh. 5 - Prob. 30ECh. 5 - Prob. 31ECh. 5 - Prob. 32ECh. 5 - Prob. 33ECh. 5 - Prob. 34ECh. 5 - Prob. 35ECh. 5 - Prob. 36ECh. 5 - Prob. 37ECh. 5 - Prob. 38ECh. 5 - Prob. 39ECh. 5 - Prob. 40ECh. 5 - Prob. 41ECh. 5 - Prob. 42ECh. 5 - Prob. 43ECh. 5 - Prob. 44ECh. 5 - Prob. 45ECh. 5 - Prob. 46ECh. 5 - Prob. 47ECh. 5 - Prob. 48ECh. 5 - Prob. 49ECh. 5 - Prob. 50ECh. 5 - Prob. 51ECh. 5 - Prob. 52ECh. 5 - Prob. 53ECh. 5 - Prob. 54ECh. 5 - Prob. 55ECh. 5 - Prob. 56ECh. 5 - Prob. 57ECh. 5 - Prob. 58ECh. 5 - Prob. 59ECh. 5 - Prob. 60ECh. 5 - Prob. 61ECh. 5 - Prob. 62ECh. 5 - Prob. 63ECh. 5 - Prob. 64ECh. 5 - Prob. 65ECh. 5 - Prob. 66ECh. 5 - Prob. 67ECh. 5 - Prob. 68ECh. 5 - Prob. 69ECh. 5 - Prob. 70ECh. 5 - Prob. 71ECh. 5 - Prob. 72ECh. 5 - Prob. 73ECh. 5 - Prob. 74ECh. 5 - Prob. 75ECh. 5 - Prob. 76ECh. 5 - Prob. 77ECh. 5 - Prob. 78ECh. 5 - Prob. 79ECh. 5 - Prob. 80ECh. 5 - Prob. 81ECh. 5 - Prob. 82ECh. 5 - Prob. 83ECh. 5 - Prob. 84ECh. 5 - Prob. 85ECh. 5 - Prob. 86ECh. 5 - Prob. 87ECh. 5 - Prob. 88ECh. 5 - Prob. 1CTCh. 5 - Prob. 2CTCh. 5 - Prob. 3CTCh. 5 - Prob. 4CTCh. 5 - Prob. 5CTCh. 5 - Prob. 6CTCh. 5 - Prob. 7CTCh. 5 - Prob. 8CTCh. 5 - Prob. 9CTCh. 5 - Prob. 10CTCh. 5 - Prob. 11CTCh. 5 - Prob. 12CTCh. 5 - Prob. 13CTCh. 5 - Prob. 14CTCh. 5 - Prob. 15CTCh. 5 - Prob. 16CTCh. 5 - Prob. 17CTCh. 5 - Prob. 18CTCh. 5 - Prob. 19CTCh. 5 - Prob. 20CTCh. 5 - Prob. 21CTCh. 5 - Prob. 22CTCh. 5 - Prob. 23CTCh. 5 - Prob. 1CCSRCh. 5 - Prob. 2CCSRCh. 5 - Prob. 3CCSRCh. 5 - Prob. 4CCSRCh. 5 - Prob. 5CCSRCh. 5 - Prob. 6CCSRCh. 5 - Prob. 7CCSRCh. 5 - Prob. 8CCSRCh. 5 - Prob. 9CCSRCh. 5 - Prob. 10CCSRCh. 5 - Prob. 11CCSRCh. 5 - Prob. 12CCSRCh. 5 - Prob. 13CCSRCh. 5 - Prob. 14CCSRCh. 5 - Prob. 15CCSRCh. 5 - Prob. 16CCSRCh. 5 - Prob. 17CCSRCh. 5 - Prob. 18CCSRCh. 5 - Prob. 19CCSRCh. 5 - Prob. 20CCSRCh. 5 - Prob. 21CCSRCh. 5 - Prob. 22CCSRCh. 5 - Prob. 23CCSR
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