Algebra 1
Algebra 1
1st Edition
ISBN: 9780078884801
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 9.5, Problem 68SR
To determine

Describe the transformations needed to obtain the graph of g(x)=x2+3 from the graph of f(x)=x26 .

Expert Solution & Answer
Check Mark

Answer to Problem 68SR

  g(x)=f(x)+9

Explanation of Solution

Given information:

  g(x)=x2+3f(x)=x26

Concept used:

Transformation of functions: For any positive integer a , we have

  • y=f(x+a) is the graph of y=f(x) shifted a units left.
  • y=f(xa) is the graph of y=f(x) shifted a units right.
  • y=f(x)+a is the graph of y=f(x) shifted a units up.
  • y=f(x)a is the graph of y=f(x) shifted a units down.
  • y=af(x) is the graph of y=f(x) stretches a units in y direction if a>1 and compresses a units in y direction if 0<a<1
  • y=f(ax) is the graph of y=f(x) stretches a units in x direction if 0<a<1 and compresses a units in x direction if a>1 .
  • y=f(x) is the graph of y=f(x) reflected about x axis.
  • y=f(x) is the graph of y=f(x) reflected about y axis.

Calculation:

In order to get the graph of g(x) from the graph of f(x) , add 9 in the function f(x) .

Observe that when the unit C is adding to the function, it will move the original f(x) graph C unit up.

So, the graph of g(x) can be obtained by shifting the graph of f(x) in upward direction by 9 units as shown below:

  f(x)=x26f(x)=x26+9f(x)=x2+3=g(x)g(x)=f(x)+9

So, the graph of g(x) can be obtained by adding 9 to the function f(x) that is g(x)=f(x)+9 .

Chapter 9 Solutions

Algebra 1

Ch. 9.1 - Prob. 77STPCh. 9.1 - Prob. 78STPCh. 9.1 - Prob. 79SRCh. 9.1 - Prob. 80SRCh. 9.1 - Prob. 81SRCh. 9.1 - Prob. 82SRCh. 9.1 - Prob. 83SRCh. 9.1 - Prob. 84SRCh. 9.1 - Prob. 85SRCh. 9.1 - Prob. 86SRCh. 9.1 - Prob. 87SRCh. 9.1 - Prob. 88SRCh. 9.1 - Prob. 89SRCh. 9.1 - Prob. 90SRCh. 9.1 - Prob. 91SRCh. 9.1 - Prob. 92SRCh. 9.1 - Prob. 38PPSCh. 9.1 - Prob. 39PPSCh. 9.1 - Prob. 40PPSCh. 9.1 - Prob. 41PPSCh. 9.1 - Prob. 42PPSCh. 9.1 - Prob. 43PPSCh. 9.1 - Prob. 44PPSCh. 9.1 - Prob. 45PPSCh. 9.1 - Prob. 46PPSCh. 9.1 - Prob. 47PPSCh. 9.1 - Prob. 48PPSCh. 9.1 - Prob. 49PPSCh. 9.1 - Prob. 50PPSCh. 9.1 - Prob. 51PPSCh. 9.1 - Prob. 52PPSCh. 9.1 - Prob. 53PPSCh. 9.1 - Prob. 54PPSCh. 9.1 - Prob. 55PPSCh. 9.1 - Prob. 56PPSCh. 9.1 - Prob. 57PPSCh. 9.1 - Prob. 58PPSCh. 9.1 - Prob. 59PPSCh. 9.1 - Prob. 60PPSCh. 9.1 - Prob. 61PPSCh. 9.1 - Prob. 62PPSCh. 9.1 - Prob. 63PPSCh. 9.1 - Prob. 64PPSCh. 9.1 - Prob. 65PPSCh. 9.1 - Prob. 66PPSCh. 9.1 - Prob. 93SCh. 9.1 - Prob. 94SCh. 9.1 - Prob. 95SCh. 9.1 - Prob. 1CYPCh. 9.1 - 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Prob. 8CYUCh. 9.8 - Prob. 9CYUCh. 9.8 - Prob. 10CYUCh. 9.8 - Prob. 11CYUCh. 9.8 - Prob. 12CYUCh. 9.8 - Prob. 13CYUCh. 9.8 - Prob. 14PPSCh. 9.8 - Prob. 15PPSCh. 9.8 - Prob. 16PPSCh. 9.8 - Prob. 17PPSCh. 9.8 - Prob. 18PPSCh. 9.8 - Prob. 19PPSCh. 9.8 - Prob. 20PPSCh. 9.8 - Prob. 21PPSCh. 9.8 - Prob. 22PPSCh. 9.8 - Prob. 23PPSCh. 9.8 - Prob. 24PPSCh. 9.8 - Prob. 25PPSCh. 9.8 - Prob. 26PPSCh. 9.8 - Prob. 27PPSCh. 9.8 - Prob. 28PPSCh. 9.8 - Prob. 29PPSCh. 9.8 - Prob. 30PPSCh. 9.8 - Prob. 31PPSCh. 9.8 - Prob. 32PPSCh. 9.9 - Prob. 1ACYPCh. 9.9 - Prob. 1BCYPCh. 9.9 - Prob. 2ACYPCh. 9.9 - Prob. 2BCYPCh. 9.9 - Prob. 3ACYPCh. 9.9 - Prob. 3BCYPCh. 9.9 - Prob. 4CYPCh. 9.9 - Prob. 1CYUCh. 9.9 - Prob. 2CYUCh. 9.9 - Prob. 3CYUCh. 9.9 - Prob. 4CYUCh. 9.9 - Prob. 5CYUCh. 9.9 - Prob. 6CYUCh. 9.9 - Prob. 7CYUCh. 9.9 - Prob. 8CYUCh. 9.9 - Prob. 9CYUCh. 9.9 - Prob. 10CYUCh. 9.9 - Prob. 11CYUCh. 9.9 - Prob. 12CYUCh. 9.9 - Prob. 13CYUCh. 9.9 - Prob. 14PPSCh. 9.9 - Prob. 15PPSCh. 9.9 - Prob. 16PPSCh. 9.9 - Prob. 17PPSCh. 9.9 - Prob. 18PPSCh. 9.9 - Prob. 19PPSCh. 9.9 - Prob. 20PPSCh. 9.9 - Prob. 21PPSCh. 9.9 - Prob. 22PPSCh. 9.9 - Prob. 23PPSCh. 9.9 - Prob. 24PPSCh. 9.9 - Prob. 25PPSCh. 9.9 - Prob. 26PPSCh. 9.9 - Prob. 27PPSCh. 9.9 - Prob. 28PPSCh. 9.9 - Prob. 29PPSCh. 9.9 - Prob. 30PPSCh. 9.9 - Prob. 31HPCh. 9.9 - Prob. 32HPCh. 9.9 - Prob. 33HPCh. 9.9 - Prob. 34HPCh. 9.9 - Prob. 36STPCh. 9.9 - Prob. 37STPCh. 9.9 - Prob. 38STPCh. 9.9 - Prob. 39STPCh. 9.9 - Prob. 40SRCh. 9.9 - Prob. 41SRCh. 9.9 - Prob. 42SRCh. 9.9 - Prob. 43SRCh. 9.9 - Prob. 44SRCh. 9.9 - Prob. 45SRCh. 9.9 - Prob. 46SRCh. 9.9 - Prob. 47SRCh. 9.9 - Prob. 48SRCh. 9.9 - Prob. 49SRCh. 9.9 - Prob. 50SRCh. 9.9 - Prob. 51SRCh. 9.9 - Prob. 52SRCh. 9.9 - Prob. 53SRCh. 9.9 - Prob. 54SRCh. 9.9 - Prob. 55SRCh. 9.9 - Prob. 56SRCh. 9.9 - Prob. 57SRCh. 9.9 - Prob. 58SRCh. 9.9 - Prob. 59SRCh. 9.9 - Prob. 60SCh. 9.9 - Prob. 61SCh. 9.9 - Prob. 62SCh. 9.9 - Prob. 35HPCh. 9 - Prob. 5STPCh. 9 - Prob. 6STPCh. 9 - Prob. 7STPCh. 9 - Prob. 8STPCh. 9 - Prob. 9STPCh. 9 - Prob. 10STPCh. 9 - Prob. 11STPCh. 9 - Prob. 1QCCh. 9 - Prob. 2QCCh. 9 - Prob. 3QCCh. 9 - Prob. 4QCCh. 9 - Prob. 5QCCh. 9 - Prob. 6QCCh. 9 - Prob. 7QCCh. 9 - Prob. 8QCCh. 9 - Prob. 9QCCh. 9 - Prob. 10QCCh. 9 - Prob. 11QCCh. 9 - Prob. 12QCCh. 9 - Prob. 13QCCh. 9 - Prob. 14QCCh. 9 - Prob. 15QCCh. 9 - Prob. 16QCCh. 9 - Prob. 17QCCh. 9 - Prob. 18QCCh. 9 - Prob. 19QCCh. 9 - Prob. 20QCCh. 9 - Prob. 1MCQCh. 9 - Prob. 2MCQCh. 9 - Prob. 3MCQCh. 9 - Prob. 4MCQCh. 9 - Prob. 5MCQCh. 9 - Prob. 6MCQCh. 9 - Prob. 7MCQCh. 9 - Prob. 8MCQCh. 9 - Prob. 9MCQCh. 9 - Prob. 10MCQCh. 9 - Prob. 11MCQCh. 9 - Prob. 12MCQCh. 9 - Prob. 13MCQCh. 9 - Prob. 14MCQCh. 9 - Prob. 15MCQCh. 9 - Prob. 16MCQCh. 9 - Prob. 17MCQCh. 9 - Prob. 18MCQCh. 9 - Prob. 19MCQCh. 9 - Prob. 20MCQCh. 9 - Prob. 21MCQCh. 9 - Prob. 22MCQCh. 9 - Prob. 23MCQCh. 9 - Prob. 24MCQCh. 9 - Prob. 25MCQCh. 9 - Prob. 1SGRCh. 9 - Prob. 2SGRCh. 9 - Prob. 3SGRCh. 9 - Prob. 4SGRCh. 9 - Prob. 5SGRCh. 9 - Prob. 6SGRCh. 9 - Prob. 7SGRCh. 9 - Prob. 8SGRCh. 9 - Prob. 9SGRCh. 9 - Prob. 10SGRCh. 9 - Prob. 11SGRCh. 9 - Prob. 12SGRCh. 9 - Prob. 13SGRCh. 9 - Prob. 14SGRCh. 9 - Prob. 15SGRCh. 9 - Prob. 16SGRCh. 9 - Prob. 17SGRCh. 9 - Prob. 18SGRCh. 9 - Prob. 19SGRCh. 9 - Prob. 20SGRCh. 9 - Prob. 21SGRCh. 9 - Prob. 22SGRCh. 9 - Prob. 23SGRCh. 9 - Prob. 24SGRCh. 9 - Prob. 25SGRCh. 9 - Prob. 26SGRCh. 9 - Prob. 27SGRCh. 9 - Prob. 28SGRCh. 9 - Prob. 29SGRCh. 9 - Prob. 30SGRCh. 9 - Prob. 31SGRCh. 9 - Prob. 32SGRCh. 9 - Prob. 33SGRCh. 9 - Prob. 34SGRCh. 9 - Prob. 35SGRCh. 9 - Prob. 36SGRCh. 9 - Prob. 37SGRCh. 9 - Prob. 38SGRCh. 9 - Prob. 39SGRCh. 9 - Prob. 40SGRCh. 9 - Prob. 41SGRCh. 9 - Prob. 42SGRCh. 9 - Prob. 43SGRCh. 9 - Prob. 44SGRCh. 9 - Prob. 45SGRCh. 9 - Prob. 46SGRCh. 9 - Prob. 47SGRCh. 9 - Prob. 48SGRCh. 9 - Prob. 49SGRCh. 9 - Prob. 50SGRCh. 9 - Prob. 51SGRCh. 9 - Prob. 52SGRCh. 9 - Prob. 53SGRCh. 9 - Prob. 54SGRCh. 9 - Prob. 55SGRCh. 9 - Prob. 56SGRCh. 9 - Prob. 57SGRCh. 9 - Prob. 58SGRCh. 9 - Prob. 59SGRCh. 9 - Prob. 60SGRCh. 9 - Prob. 61SGRCh. 9 - Prob. 62SGRCh. 9 - Prob. 63SGRCh. 9 - Prob. 1PTCh. 9 - Prob. 2PTCh. 9 - Prob. 3PTCh. 9 - Prob. 4PTCh. 9 - Prob. 5PTCh. 9 - Prob. 6PTCh. 9 - Prob. 7PTCh. 9 - Prob. 8PTCh. 9 - Prob. 9PTCh. 9 - Prob. 10PTCh. 9 - Prob. 11PTCh. 9 - Prob. 12PTCh. 9 - Prob. 13PTCh. 9 - Prob. 14PTCh. 9 - Prob. 15PTCh. 9 - Prob. 16PTCh. 9 - Prob. 17PTCh. 9 - Prob. 18PTCh. 9 - Prob. 19PTCh. 9 - Prob. 20PTCh. 9 - Prob. 21PTCh. 9 - Prob. 22PTCh. 9 - Prob. 23PTCh. 9 - Prob. 24PTCh. 9 - Prob. 25PTCh. 9 - Prob. 26PTCh. 9 - Prob. 27PTCh. 9 - Prob. 28PTCh. 9 - Prob. 1STPCh. 9 - Prob. 2STPCh. 9 - Prob. 3STPCh. 9 - Prob. 4STP
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