   Chapter 2.2, Problem 11E

Chapter
Section
Textbook Problem

Sketch the graph of the function and use it to determine the values of a for which lim x → a f(x) exists. f ( x ) = { 1 + x     if   x < − 1 x 2     if   − 1 ≤ x < 1 2 − x     if   x ≥ 1

To determine

To sketch: The graph of f(x) and determine the value of a from the graph for which limxaf(x) exists.

Explanation

Given:

The function f(x)={1+xif x<1x2if 1x<12xif x1.

Graph:

Draw a parabola of y=x2 between the interval 1x<1 and draw a ray of y=2x starting at the point (1, 1) on a given interval x1 and draw a ray of y=2x on a interval x<1.

The graph of f(x) is shown below in Figure 1

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