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Chapter 2: Q47. (page 104)

Graph each function. Identify the domain and range

47.鈥夆赌夆赌�fx=鈥夆赌夆赌夆�夆赌夆赌夆�夆赌�2鈥夆赌夆赌夆�夆赌夆赌�if鈥夆赌�x<鈭�1鈭�x鈭�1鈥夆赌夆赌�if鈥夆赌�x鈮�鈭�1

Short Answer

Expert verified

The graph of the function is as shown,

The function is defined for all value of x so that domain is all real numbers.

The range is y=2

Step by step solution

01

Step-1 – Graph the constant function first

fx=2鈥�鈥�for鈥�鈥�x<-1鈥�鈥� at -1,2

02

Step-2 – Graph the linear function 

Graph the linear function fx=-x-1鈥�for鈥�鈥�x鈮�-1鈥�鈥�

Since -1does not satisfy the inequality at -1,0

03

Step-3 –Identify the domain and range

The function is defined for all value of x so that domain is all real numbers.

The range is y=2

04

Step-4 – Plot the graph

Hence, the graph of function is as shown.

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