Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Question
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Chapter 6.6, Problem 52STP

a.

To determine

To calculate: the x -coordinate of every turning point and also determine whether the coordinates are relative maximum or relative minima.

a.

Expert Solution
Check Mark

Answer to Problem 52STP

  2(maximum),3(maximum),0(minimum),3.5(minimum) .

Explanation of Solution

Given information:

  Algebra 2, Chapter 6.6, Problem 52STP , additional homework tip  1

Formula used:

Relative maximum- The point on the graph is a relative maximum of the function when there is no other nearby points that have greater y -coordinate.

Relative minimum- The point on the graph is a relative minimum of the function when there is no other nearby points that have lesser y -coordinate.

Calculation:

According to the graph ,

We observed four turning points 2,0,3 and 3.5 at which the function changes.

At point x=2 , the value of function is greater than the surrounding points, so there must be relative maximum.

At point x=3 , the value of function is greater than the surrounding points, so there must be relative maximum.

At point x=0 , the value of function is lesser than the surrounding points, so there must be relative minimum .

At point x=3.5 , the value of function is lesser than the surrounding points, so there must be relative minimum .

Hence, the following are the x -coordinate 2(maximum),3(maximum),0(minimum),3.5(minimum) .

b.

To determine

To calculate: the x -coordinate of every zero.

b.

Expert Solution
Check Mark

Answer to Problem 52STP

The x -coordinate of every zero are x=1,x=3.8,x=1.5,x=3.5 and x=3.7 .

Explanation of Solution

Given information:

  Algebra 2, Chapter 6.6, Problem 52STP , additional homework tip  2

Formula used:

The changes in sign indicate that there are zeros between those two x -values.

Calculations:

According to the graph ,

We observed four turning points 2,0,3 and 3.5 at which the function changes.

The graph crosses the x -axis at five points.

At x=1,x=3.8,x=1.5,x=3.5 and x=3.7 .

Hence, the x -coordinate of every zero are x=1,x=3.8,x=1.5,x=3.5 and x=3.7 .

c.

To determine

To calculate: the smallest possible degree of the function.

c.

Expert Solution
Check Mark

Answer to Problem 52STP

Smallest degree of the function is 5.

Explanation of Solution

Given information:

  Algebra 2, Chapter 6.6, Problem 52STP , additional homework tip  3

Formula used:

The maximum and minimum values of a function are called extrema .

These points are referred to as turning points.

The graph of the polynomial function of degree n has at most n1 turning points.

Calculation:

According to the graph ,

We observed four turning points at which the function changes.

Hence, the smallest possible degree of the function is 5.

d.

To determine

To calculate: the domain and range of the function .

d.

Expert Solution
Check Mark

Answer to Problem 52STP

The domain and range of the function are all real numbers and {y|y4}{y|y2} respectively.

Explanation of Solution

Given information:

  Algebra 2, Chapter 6.6, Problem 52STP , additional homework tip  4

Formula used:

Domain of the function : is the set of all values for which function is defined.

Range of the function : is the set of all values that f takes.

Calculation:

According to the graph ,

Domain is presented by x -axis. This implies domain is all real numbers.

Range is presented by y -axis. This implies {y|y4}{y|y2} .

Hence, the domain and range of the function are all real numbers and {y|y4}{y|y2} respectively.

Chapter 6 Solutions

Algebra 2

Ch. 6.1 - Prob. 5CYPCh. 6.1 - Prob. 6ACYPCh. 6.1 - Prob. 6BCYPCh. 6.1 - Prob. 1CYUCh. 6.1 - Prob. 2CYUCh. 6.1 - Prob. 3CYUCh. 6.1 - Prob. 4CYUCh. 6.1 - Prob. 5CYUCh. 6.1 - Prob. 6CYUCh. 6.1 - Prob. 7CYUCh. 6.1 - Prob. 8CYUCh. 6.1 - Prob. 9CYUCh. 6.1 - Prob. 10CYUCh. 6.1 - Prob. 11CYUCh. 6.1 - Prob. 12CYUCh. 6.1 - Prob. 13CYUCh. 6.1 - Prob. 14CYUCh. 6.1 - Prob. 15CYUCh. 6.1 - Prob. 16PPSCh. 6.1 - Prob. 17PPSCh. 6.1 - Prob. 18PPSCh. 6.1 - Prob. 19PPSCh. 6.1 - Prob. 20PPSCh. 6.1 - Prob. 21PPSCh. 6.1 - Prob. 22PPSCh. 6.1 - Prob. 23PPSCh. 6.1 - Prob. 24PPSCh. 6.1 - Prob. 25PPSCh. 6.1 - Prob. 26PPSCh. 6.1 - Prob. 27PPSCh. 6.1 - Prob. 28PPSCh. 6.1 - Prob. 29PPSCh. 6.1 - Prob. 30PPSCh. 6.1 - Prob. 31PPSCh. 6.1 - Prob. 32PPSCh. 6.1 - Prob. 33PPSCh. 6.1 - Prob. 34PPSCh. 6.1 - Prob. 35PPSCh. 6.1 - Prob. 36PPSCh. 6.1 - Prob. 37PPSCh. 6.1 - Prob. 38PPSCh. 6.1 - Prob. 39PPSCh. 6.1 - Prob. 40PPSCh. 6.1 - Prob. 41PPSCh. 6.1 - Prob. 42PPSCh. 6.1 - Prob. 43PPSCh. 6.1 - Prob. 44PPSCh. 6.1 - Prob. 45PPSCh. 6.1 - 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Prob. 43HPCh. 6.6 - Prob. 44HPCh. 6.6 - Prob. 45HPCh. 6.6 - Prob. 46HPCh. 6.6 - Prob. 47HPCh. 6.6 - Prob. 48STPCh. 6.6 - Prob. 49STPCh. 6.6 - Prob. 50STPCh. 6.6 - Prob. 51STPCh. 6.6 - Prob. 52STPCh. 6.6 - Prob. 53STPCh. 6.6 - Prob. 54STPCh. 6.6 - Prob. 55STPCh. 6.6 - Prob. 56STPCh. 6.6 - Prob. 57STPCh. 6.6 - Prob. 58SCh. 6.6 - Prob. 59SCh. 6.6 - Prob. 60SCh. 6.6 - Prob. 61SCh. 6.6 - Prob. 62SCh. 6.6 - Prob. 63SCh. 6.7 - Prob. 1ACYPCh. 6.7 - Prob. 1BCYPCh. 6.7 - Prob. 1CCYPCh. 6.7 - Prob. 1DCYPCh. 6.7 - Prob. 2CYPCh. 6.7 - Prob. 3CYPCh. 6.7 - Prob. 4CYPCh. 6.7 - Prob. 1CYUCh. 6.7 - Prob. 2CYUCh. 6.7 - Prob. 3CYUCh. 6.7 - Prob. 4CYUCh. 6.7 - Prob. 5CYUCh. 6.7 - Prob. 6CYUCh. 6.7 - Prob. 7CYUCh. 6.7 - Prob. 8CYUCh. 6.7 - Prob. 9CYUCh. 6.7 - Prob. 10CYUCh. 6.7 - Prob. 11CYUCh. 6.7 - Prob. 12CYUCh. 6.7 - Prob. 13CYUCh. 6.7 - Prob. 14CYUCh. 6.7 - Prob. 15CYUCh. 6.7 - Prob. 16CYUCh. 6.7 - Prob. 17PPSCh. 6.7 - Prob. 18PPSCh. 6.7 - Prob. 19PPSCh. 6.7 - Prob. 20PPSCh. 6.7 - Prob. 21PPSCh. 6.7 - Prob. 22PPSCh. 6.7 - Prob. 23PPSCh. 6.7 - Prob. 24PPSCh. 6.7 - Prob. 25PPSCh. 6.7 - Prob. 26PPSCh. 6.7 - Prob. 27PPSCh. 6.7 - Prob. 28PPSCh. 6.7 - Prob. 29PPSCh. 6.7 - Prob. 30PPSCh. 6.7 - Prob. 31PPSCh. 6.7 - Prob. 32PPSCh. 6.7 - Prob. 33PPSCh. 6.7 - Prob. 34PPSCh. 6.7 - Prob. 35PPSCh. 6.7 - Prob. 36PPSCh. 6.7 - Prob. 37PPSCh. 6.7 - Prob. 38PPSCh. 6.7 - Prob. 39PPSCh. 6.7 - Prob. 40PPSCh. 6.7 - Prob. 41PPSCh. 6.7 - Prob. 42PPSCh. 6.7 - Prob. 43PPSCh. 6.7 - Prob. 44PPSCh. 6.7 - Prob. 45PPSCh. 6.7 - Prob. 46PPSCh. 6.7 - Prob. 47PPSCh. 6.7 - Prob. 48PPSCh. 6.7 - Prob. 49PPSCh. 6.7 - Prob. 50PPSCh. 6.7 - Prob. 51PPSCh. 6.7 - Prob. 52PPSCh. 6.7 - Prob. 53PPSCh. 6.7 - Prob. 54PPSCh. 6.7 - Prob. 55PPSCh. 6.7 - Prob. 56HPCh. 6.7 - Prob. 57HPCh. 6.7 - Prob. 58HPCh. 6.7 - Prob. 59HPCh. 6.7 - Prob. 60HPCh. 6.7 - Prob. 61HPCh. 6.7 - Prob. 62HPCh. 6.7 - Prob. 63HPCh. 6.7 - Prob. 64HPCh. 6.7 - Prob. 65STPCh. 6.7 - Prob. 66STPCh. 6.7 - Prob. 67STPCh. 6.7 - Prob. 68STPCh. 6.7 - Prob. 69STPCh. 6.7 - Prob. 70STPCh. 6.7 - Prob. 71STPCh. 6.7 - Prob. 72STPCh. 6.7 - Prob. 73STPCh. 6.7 - Prob. 74SCh. 6.7 - Prob. 75SCh. 6.7 - Prob. 76SCh. 6.8 - Prob. 1ACYPCh. 6.8 - Prob. 1BCYPCh. 6.8 - Prob. 2CYPCh. 6.8 - Prob. 3ACYPCh. 6.8 - Prob. 3BCYPCh. 6.8 - Prob. 1CYUCh. 6.8 - Prob. 2CYUCh. 6.8 - Prob. 3CYUCh. 6.8 - Prob. 4CYUCh. 6.8 - Prob. 5CYUCh. 6.8 - Prob. 6CYUCh. 6.8 - Prob. 7CYUCh. 6.8 - Prob. 8CYUCh. 6.8 - Prob. 9CYUCh. 6.8 - Prob. 10PPSCh. 6.8 - Prob. 11PPSCh. 6.8 - Prob. 12PPSCh. 6.8 - Prob. 13PPSCh. 6.8 - Prob. 14PPSCh. 6.8 - Prob. 15PPSCh. 6.8 - Prob. 16PPSCh. 6.8 - Prob. 17PPSCh. 6.8 - Prob. 18PPSCh. 6.8 - Prob. 19PPSCh. 6.8 - Prob. 20PPSCh. 6.8 - Prob. 21PPSCh. 6.8 - Prob. 22PPSCh. 6.8 - Prob. 23PPSCh. 6.8 - Prob. 24PPSCh. 6.8 - Prob. 25PPSCh. 6.8 - Prob. 26PPSCh. 6.8 - Prob. 27PPSCh. 6.8 - Prob. 28PPSCh. 6.8 - Prob. 29PPSCh. 6.8 - Prob. 30PPSCh. 6.8 - Prob. 31PPSCh. 6.8 - Prob. 32PPSCh. 6.8 - Prob. 33PPSCh. 6.8 - Prob. 34PPSCh. 6.8 - Prob. 35PPSCh. 6.8 - Prob. 36PPSCh. 6.8 - Prob. 37PPSCh. 6.8 - Prob. 38PPSCh. 6.8 - Prob. 39PPSCh. 6.8 - Prob. 40PPSCh. 6.8 - Prob. 41PPSCh. 6.8 - Prob. 42PPSCh. 6.8 - Prob. 43PPSCh. 6.8 - Prob. 44PPSCh. 6.8 - Prob. 45PPSCh. 6.8 - Prob. 46HPCh. 6.8 - Prob. 47HPCh. 6.8 - Prob. 48HPCh. 6.8 - Prob. 49HPCh. 6.8 - Prob. 50HPCh. 6.8 - Prob. 51HPCh. 6.8 - Prob. 52HPCh. 6.8 - Prob. 53HPCh. 6.8 - Prob. 54HPCh. 6.8 - Prob. 55HPCh. 6.8 - Prob. 56STPCh. 6.8 - Prob. 57STPCh. 6.8 - Prob. 58STPCh. 6.8 - Prob. 59STPCh. 6.8 - Prob. 60STPCh. 6.8 - Prob. 61STPCh. 6.8 - Prob. 62STPCh. 6.8 - Prob. 63STPCh. 6.8 - Prob. 64SCh. 6.8 - Prob. 65SCh. 6.8 - Prob. 66SCh. 6.8 - Prob. 67SCh. 6.8 - Prob. 68SCh. 6.8 - Prob. 69SCh. 6.8 - Prob. 1SGRCh. 6.8 - Prob. 2SGRCh. 6.8 - Prob. 3SGRCh. 6.8 - Prob. 4SGRCh. 6.8 - Prob. 5SGRCh. 6.8 - Prob. 6SGRCh. 6.8 - Prob. 7SGRCh. 6.8 - Prob. 8SGRCh. 6.8 - Prob. 9SGRCh. 6.8 - Prob. 10SGRCh. 6.8 - Prob. 11SGRCh. 6.8 - Prob. 12SGRCh. 6.8 - Prob. 13SGRCh. 6.8 - Prob. 14SGRCh. 6.8 - Prob. 15SGRCh. 6.8 - Prob. 16SGRCh. 6.8 - Prob. 17SGRCh. 6.8 - Prob. 18SGRCh. 6.8 - Prob. 19SGRCh. 6.8 - Prob. 20SGRCh. 6.8 - Prob. 21SGRCh. 6.8 - Prob. 22SGRCh. 6.8 - Prob. 23SGRCh. 6.8 - Prob. 24SGRCh. 6.8 - Prob. 25SGRCh. 6.8 - Prob. 26SGRCh. 6.8 - Prob. 27SGRCh. 6.8 - Prob. 28SGRCh. 6.8 - Prob. 29SGRCh. 6.8 - Prob. 30SGRCh. 6.8 - Prob. 31SGRCh. 6.8 - Prob. 32SGRCh. 6.8 - Prob. 33SGRCh. 6.8 - Prob. 34SGRCh. 6.8 - Prob. 35SGRCh. 6.8 - Prob. 36SGRCh. 6.8 - Prob. 37SGRCh. 6.8 - Prob. 38SGRCh. 6.8 - Prob. 39SGRCh. 6.8 - Prob. 40SGRCh. 6.8 - Prob. 41SGRCh. 6.8 - Prob. 42SGRCh. 6.8 - Prob. 43SGRCh. 6.8 - Prob. 44SGRCh. 6.8 - Prob. 45SGRCh. 6.8 - Prob. 46SGRCh. 6.8 - Prob. 47SGRCh. 6.8 - Prob. 48SGRCh. 6.8 - Prob. 49SGRCh. 6.8 - Prob. 50SGRCh. 6.8 - Prob. 51SGRCh. 6.8 - Prob. 52SGRCh. 6.8 - Prob. 53SGRCh. 6.8 - Prob. 54SGRCh. 6.8 - Prob. 55SGRCh. 6.8 - Prob. 56SGRCh. 6.8 - Prob. 1PTCh. 6.8 - Prob. 2PTCh. 6.8 - Prob. 3PTCh. 6.8 - Prob. 4PTCh. 6.8 - Prob. 5PTCh. 6.8 - Prob. 6PTCh. 6.8 - Prob. 7PTCh. 6.8 - Prob. 8PTCh. 6.8 - Prob. 9PTCh. 6.8 - Prob. 10PTCh. 6.8 - Prob. 11PTCh. 6.8 - Prob. 12PTCh. 6.8 - Prob. 13PTCh. 6.8 - Prob. 14PTCh. 6.8 - Prob. 15PTCh. 6.8 - Prob. 16PTCh. 6.8 - Prob. 17PTCh. 6.8 - Prob. 18PTCh. 6.8 - Prob. 19PTCh. 6.8 - Prob. 20PTCh. 6.8 - Prob. 21PTCh. 6.8 - Prob. 22PTCh. 6.8 - Prob. 23PTCh. 6.8 - Prob. 24PTCh. 6.8 - Prob. 25PTCh. 6.8 - Prob. 1ECh. 6.8 - Prob. 2ECh. 6.8 - Prob. 1STPCh. 6.8 - Prob. 2STPCh. 6.8 - Prob. 3STPCh. 6.8 - Prob. 4STPCh. 6.8 - Prob. 5STPCh. 6.8 - Prob. 6STPCh. 6.8 - Prob. 7STPCh. 6.8 - Prob. 8STPCh. 6.8 - Prob. 9STPCh. 6.8 - Prob. 10STPCh. 6.8 - Prob. 11STPCh. 6.8 - Prob. 12STPCh. 6.8 - Prob. 13STPCh. 6.8 - Prob. 14STPCh. 6.8 - Prob. 15STPCh. 6.8 - Prob. 16STPCh. 6.8 - Prob. 17STPCh. 6 - Prob. 1QCCh. 6 - Prob. 2QCCh. 6 - Prob. 3QCCh. 6 - Prob. 4QCCh. 6 - Prob. 5QCCh. 6 - Prob. 6QCCh. 6 - Prob. 7QCCh. 6 - Prob. 8QCCh. 6 - Prob. 9QCCh. 6 - Prob. 10QCCh. 6 - Prob. 11QCCh. 6 - Prob. 12QCCh. 6 - Prob. 13QCCh. 6 - Prob. 14QCCh. 6 - Prob. 15QCCh. 6 - Prob. 1MCQCh. 6 - Prob. 2MCQCh. 6 - Prob. 3MCQCh. 6 - Prob. 4MCQCh. 6 - Prob. 5MCQCh. 6 - Prob. 6MCQCh. 6 - Prob. 7MCQCh. 6 - Prob. 8MCQCh. 6 - Prob. 9MCQCh. 6 - Prob. 10MCQCh. 6 - Prob. 11MCQCh. 6 - Prob. 12MCQCh. 6 - Prob. 13MCQCh. 6 - Prob. 14MCQCh. 6 - Prob. 15MCQCh. 6 - Prob. 16MCQCh. 6 - Prob. 17MCQCh. 6 - Prob. 18MCQCh. 6 - Prob. 19MCQCh. 6 - Prob. 20MCQCh. 6 - Prob. 21MCQ
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