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Chapter 4: Q. 31 (page 245)

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

R(x)=x+2x2-9

Short Answer

Expert verified

The domain of the function is x|x鈮�-3,x鈮�3and vertical asymptotes are x=3,x=-3and horizontal asymptote isy=0

Step by step solution

01

Step 1. Given Information

The given function isR(x)=x+2x2-9

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 x2-9=0and solve.

x2-9=0(x+3)(x-3)=0x=-3,3

03

Step 3. Explanation

The vertical asymptote is the point at which x2-9=0

Thus, the vertical asymptotes are x=-3,3

If a rational function is proper, then y=0is a horizontal asymptote of the graph of rational function.

Thus, horizontal asymptote isy=0

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