   Chapter 1, Problem 6P ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Sketch the graph of the function g(x) = |x2 –1 | – |x2 – 4|.

To determine

To sketch: The function g(x)=|x21||x24|.

Explanation

Given:

The function g(x)=|x21||x24|.

Result used:

Even function:

A function is even if and only if g(x)=g(x) for all x in the domain of g.

Definition used:

The absolute value of x is defined as, |x|={xif x0xif x<0.

Calculation:

Consider the function g(x)=|x21||x24|

Now, |x21|={x21ifx11x2ifx<1

|x24|={x24ifx24x2ifx<2

The function can be split into different cases as follows:

Case (i):

For 0x1

g1(x)=x2+1x24g1(x)=3

To sketch: Use the online graphing calculator and draw the graph of the function: g1(x)=3 as shown below in Figure 1.

Case (ii):

For 1x<2

g2(x)=x21+x24g2(x)=2x25

To sketch: Use the online graphing calculator and draw the graph of the function: g2(x)=2x2+5 as shown below in Figure 2

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