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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Chapter
Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Use the guidelines of Section 4.5 to sketch the curve.

y = x 1 x 2

To determine

To sketch: The curve by plotting x and y coordinates using guidelines of section 4.5.

Explanation

Given:

The Cartesian equation is, y=x1x2 (1)

Calculation:

a)

Calculate the domain:

Refer the equation (1), the function is defined for all real values of x except for x=±1 Hence, the domain of f(x) is \{1,1}.

b)

Calculate the intercepts:

Calculate the value of x-intercept as follows.

Substitute 0 for y in the equation (1),

0=x1x2x=0

Hence the x-intercept is (0,0).

Calculate the y-intercept.

Substitute 0 for x in the equation (1),

y=0102=0

Therefore, the y-intercept is (0,0).

c)

Calculate the symmetry:

Apply negative and positive values for x in the equation (1).

Substitute x in the equation (1),

f(x)=x1x2f(x)=x1(x)2=x1x2

Hence, the condition f(x)=f(x) is true. So, the graph of f is symmetric about origin.

d)

Calculate the asymptotes:

Apply the limit that x tends to in the equation (1),

limxy=limxx1x2=limx1x1x21=001=0

Hence, y=0 is an horizontal asymptote

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