Holt Mcdougal Larson Algebra 2: Student Edition 2012
Holt Mcdougal Larson Algebra 2: Student Edition 2012
1st Edition
ISBN: 9780547647159
Author: HOLT MCDOUGAL
Publisher: HOLT MCDOUGAL
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Expert Solution & Answer
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Chapter 3.1, Problem 65PS
Solution

(a)

To explain how the given graph justifies the results in the Key Concept box when n is a positive even integer.

  25.44 cm

Given:

The graph of y=xn for any positive even integer n .

  Holt Mcdougal Larson Algebra 2: Student Edition 2012, Chapter 3.1, Problem 65PS , additional homework tip  1

And the Key Concept box,

  Holt Mcdougal Larson Algebra 2: Student Edition 2012, Chapter 3.1, Problem 65PS , additional homework tip  2

Concept Used:

  • The even inter root of a number is defined for positive values only that are greater than or equal to 0.
  • The odd integer root of all real numbers is defined.
  • Power of a power property: xab=xab
  • The exponent form of the nth root of a number a is given by an=a1n

Calculation:

From the given graph, note that the line y=a for a<0 does not intersect the graph of y=xn at any point, so there is no solution when the value of a is negative.

Also, note that the line y=0 touches the graph of y=xn at one point only, so there is only one solution when a=0 .

And, the line y=a for a>0 intersects the graph of y=xn at two different points, so there are two solutions when the value of a is positive.

(b)

To draw a graph that justifies the results in the Key concept box when n is a positive odd integer.

  Holt Mcdougal Larson Algebra 2: Student Edition 2012, Chapter 3.1, Problem 65PS , additional homework tip  3

Given:

The Key Concept box,

  Holt Mcdougal Larson Algebra 2: Student Edition 2012, Chapter 3.1, Problem 65PS , additional homework tip  4

Concept Used:

  • The even inter root of a number is defined for positive values only that are greater than or equal to 0.
  • The odd integer root of all real numbers is defined.
  • Power of a power property: xab=xab
  • The exponent form of the nth root of a number a is given by an=a1n

Calculation:

The graph that justifies the results in the Key Concept box when n is a positive odd integer is shown below

  Holt Mcdougal Larson Algebra 2: Student Edition 2012, Chapter 3.1, Problem 65PS , additional homework tip  5

Chapter 3 Solutions

Holt Mcdougal Larson Algebra 2: Student Edition 2012

Ch. 3.1 - Prob. 11GPCh. 3.1 - Prob. 12GPCh. 3.1 - Prob. 13GPCh. 3.1 - Prob. 14GPCh. 3.1 - Prob. 15GPCh. 3.1 - Prob. 16GPCh. 3.1 - Prob. 17GPCh. 3.1 - Prob. 18GPCh. 3.1 - Prob. 19GPCh. 3.1 - Prob. 1ECh. 3.1 - Prob. 2ECh. 3.1 - Prob. 3ECh. 3.1 - Prob. 4ECh. 3.1 - Prob. 5ECh. 3.1 - Prob. 6ECh. 3.1 - Prob. 7ECh. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10ECh. 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 - 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