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Chapter 4: Q. 6 (page 247)

Find the domain of each function. Find any horizontal, vertical, or oblique asymptotes.

r(x)=x2+2x-3x+1

Short Answer

Expert verified

The domain of the function is x|x鈮�1, vertical asymptote is x=-1 and oblique asymptote is aty=x-1

Step by step solution

01

Step 1. Given Information

The given function isr(x)=x2+2x-3x+1

02

Step 2. Calculation 

Substitute the denominator expression equal to 0 to find the domain.

x+1=0x=-1

Thus, the domain of the function isx|x鈮�-1

03

Step 3. Calculation 

The zeroes of denominator x+1is -1

Thus, line x=-1is the vertical asymptote.

The rational function is improper since degree of numerator is greater than the degree of denominator.

We will be using the long division method to express the function as P(x)=f(x)+r(x)q(x)

Thus, P(x)=x-1+-2x+1

As x鈫�鈭�orx鈫�-鈭�,

-2x+1鈮�-2x鈫�0

Thus,P(x)鈫�x-1. The oblique asymptote is aty=x-1

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Most popular questions from this chapter

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

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Ct=t2t2+1

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