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Chapter 4: Q. 49 (page 225)

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

Q(x)=2x2-5x-123x2-11x-4

Short Answer

Expert verified

y=23will be the horizontal asymptote for given rational expression.

Step by step solution

01

Step 1. Given information

Given rational expression:

Q(x)=2x2-5x-123x2-11x-4

02

Step 2. Write the concept

If n = m (the degree of the numerator equals the degree of the denominator), the quotient obtained will be

the number anbm, and the line y=anbmis a horizontal asymptote.

03

Step 3. Calculation

Here,n=2,m=2

Now

F(x)=2x2-5x-123x2-11x-4Takingx2commonfromnumeratoranddenominatorweget=limx鈫�鈭�x2(2-5xx2-12x2)x2(3-11xx2-4x2)=23i.eanbm=23

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Most popular questions from this chapter

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

f(x)=4x5+12x4-x-3

Find the domain of the rational function.

R(x)=5x23+x

Graph each rational function using transformations.

F(x)=2-1x+1

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

Find the real zeros of f. Use the real zeros to factor f.

f(x)=x3+6x2+6x-4
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