   Chapter 2.4, Problem 17E

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.17. f ( x ) = { x − 1 if  x ≤ 0 − 1 if  x > 0 (a = 0)

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

Explanation

Given:

The given function is f(x)={x1,ifx01,ifx>0 and the value of a is 0.

Calculation:

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

For x0 , function is f(x)=x1 . The values of a function are summarized in the below table.

 x f(x)=x−1 0 −1 −1 −2

For x>0 , function is f(x)=1 . The function is constant for values less than 0, so for any value of x less than 0, the value of function is 1

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