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Chapter 4: Q. 45 (page 225)

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.

H(x)=x3-8x2-5x+6

Short Answer

Expert verified

y=x+5will be oblique asymptote for the given rational expression.

Step by step solution

01

Step 1. Given information

Given rational expression:

H(x)=x3-8x2-5x+6

02

Step 2. Write the concept

If n = m + 1 (the degree of the numerator is one more than the degree of the denominator), the

quotient obtained is of the form ax + b (a polynomial of degree 1), and the line y = ax + b is an oblique

asymptote.

03

Step 3. Calculation

Here,n=3,m=2

Therefore, n=m+1and

therefore,

y=ax+bwillbeobliqueasymptotey=x+5

i.e. the quotient when we divide numerator with denominator.

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Most popular questions from this chapter

Find the domain of the rational function.

R(x)=5x23+x

Find the bounds to the zeros of each polynomial function. Use the bounds to obtain a complete graph of f.

f(x)=2x3-x2-11x-6

In Problems 21鈥�32, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros.

f(x)=2x5-x4-x2+1

In Problems 39鈥�56, find the real zeros of f. Use the real zeros to factor f.

f(x)=4x4+7x2-2

True or False. The graph of a rational function may intersect

a horizontal asymptote.
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