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Chapter 4: Q. 50 (page 225)

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

F(x)=x2+6x+52x2+7x+5

Short Answer

Expert verified

y=12will be the horizontal asymptote for given rational expression.

Step by step solution

01

Step 1. Given information

Given rational expression:

F(x)=x2+6x+52x2+7x+5

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=2thus,n=m

Now

F(x)=x2+6x+52x2+7x+5Takingx2commonfromnumeratoranddenominatorweget=limx鈫�鈭�x2(1+6xx2+5x2)x2(2+7xx2+5x2)=12i.eanbm=12

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Most popular questions from this chapter

Solve the given inequality algebraically.

x+1x-1>0

In Problems 63鈥�72, find the real solutions of each equation.

3x3+4x2-7x+2=0

In Problems 57鈥� 62, find the real zeros of f. If necessary, round to two decimal places.

f(x)=x3+42.2x2-664.8x+1490.4

Find a rational function that might have the given graph.

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

f(x)=3x3-7x2+12x-28
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