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 50E
To determine

To write the equation of the final transformed graph.

Expert Solution

Answer to Problem 50E

The equation of the final transformed graph is g(x)=|x+4|2 .

Explanation of Solution

Given information :

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

Concept used:

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

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

The graph of g(x) is obtained by shifting left the graph of f(x)=|x| by 4 units and then shift 2 unit downward.

Use definition of horizontallyand vertically shifting of the graph,

Therefore,

The equation of the final transformed graph is obtained as:

  g(x)=f(x+c)d

Substitute, f(x)=|x| and c=4 , d=2

  g(x)=|x+4|2

Hence,

The equation of the final transformed graph is g(x)=|x+4|2 .

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!