BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 2.5, Problem 54E
To determine

To write the equation of the final transformed graph.

Expert Solution

Answer to Problem 54E

The equation of the final transformed graph is g(x)=12|x1|+3 .

Explanation of Solution

Given information :

The function is f(x)=|x| .

Concept used:

If the graph of y=f(x) is shifted horizontallyright by c unit, then the equation of the transformed graph will be g(x)=f(xc)

If the graph of y=f(x) is shifted vertically upward by c unit, then the equation of the transformed graph will be g(x)=f(x)+c .

If the graph of y=f(x) is shrink vertically by a factor of c unit, then the equation of the transformed graph will be g(x)=cf(x) .

The function is given as: f(x)=|x|

The graph of g(x) is obtained by shrink the graph of f(x)=|x| vertically by a factor of 12 unit then shift 1 unitsright and then shift 3 unit upwards.

Use definition of horizontally, vertically shifting and shrinking vertically of the graph,

Therefore,

The equation of the final transformed graph is obtained as:

  g(x)=d·f(xc)+e

Substitute, f(x)=|x| and c=1,d=12 and e=3 ,

  g(x)=12|x1|+3

Hence,

The equation of the final transformed graph is g(x)=12|x1|+3 .

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