   Chapter 2.1, Problem 49E

Chapter
Section
Textbook Problem

In Exercises 39-50, sketch the graph of the function with the given rule. Find the domain and range of the function.49. f ( x ) = { − x + 1 if  x < 2 x 2 − 1 if  x > 1

To determine

To sketch: The graph of function f(x)={x+1ifx1x21if   x>1 .

Explanation

The given function is a piecewise defined function. For sub domain x1 or (,1] it is defined as f(x)=x+1 and for sub domain x>1 or [0,) it is defined as f(x)=x21 .

Find the points on both the graph of the given function in their respective domains.

Graph:

The given function for sub domain x1 is,

f(x)=x+1 (1)

Substitute some values of x from (,1] in equation (1) and find the corresponding values of f(x) as given in the below table.

 x f(x)=−x+1 −1 2 −2 3 −3 4

The points on the curve f(x)=x+1 from above table are (1,2),(2,3) and (3,4)

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