   Chapter 2.4, Problem 19E

Chapter
Section
Textbook Problem

In Exercises 17-22, sketch the graph of the function f and evaluate lim x → a f ( x ) , if it exists, for the given value of a.19. f ( x ) = { x if  x < 1 0 if  x = 1 − x + 2 if  x > 1 (a = 1)

To determine

To draw: The graph of a given function and determine the value of limxaf(x) for the indicated value of a.

Explanation

The given function is f(x)={x,ifx<10,ifx=1x+2,ifx>1(a=1) .

To sketch the graph, find values of f(x) for different values of x.

For x<1 , function is f(x)=x . The values of a function are summarized in table.

 x f(x)=x −1 −1 0 0

For x=1 , function is f(x)=0 . The value of a function is 0, at x=1 .

For x>1 , function is f(x)=x+2 . The values of a function are summarized in table.

 x f(x)=−x+2 2 0 3 −1

Plot all the coordinate points and join them by straight lines

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