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Chapter 4: Q. 44 (page 225)

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

R(x)=3x+5x-6

Short Answer

Expert verified

y=3 is the horizontal asymptote for the given rational expression.

Step by step solution

01

Step 1. Given information

Given rational expression:

R(x)=3x+5x-6

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=1,m=1

Now,

R(x)=3x+5x-6Takingxcommonweget=limx鈫�鈭�x(3+5x)x(1-6x)=3

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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)=4x4+15x2-4

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

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

Solve each inequality algebraically.

x-3x+1>0

In Problems63鈥�72, find the real solutions of each equation.

2x3-11x2+10x+8=0

In Problems 7-44, follow Steps 1through 7 on page 228to analyze the graph of each function.

G(x)=x3+1x2+2x
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