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Chapter 4: Q. 32 (page 245)

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

R(x)=x2+3x+2(x+2)2

Short Answer

Expert verified

The domain of the function is x|x鈮�-2and vertical asymptotes is x=-2 and horizontal asymptote is y=1

Step by step solution

01

Step 1. Given Information

The given function isR(x)=x2+3x+2(x+2)2

02

Step 2. Explanation 

The domain of the function is the set of all real numbers except for all those values for which denominator is 0.

Substitute (x+2)2=0and solve.

(x+2)2=0 x+2=0x=-2

The vertical asymptote is the point at which (x+2)2=0

Thus, the vertical asymptote is x=-2

The horizontal asymptote can be found by dividing the leading coefficients of the numerator and denominator.

Thus, horizontal asymptote is

y=11y=1

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