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Chapter 4: Q. 5 (page 247)

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

g(x)=2x2-14x+24x2+6x-40

Short Answer

Expert verified

The domain of the function isx|x鈮�-10,4, vertical asymptote isx=-10and horizontal asymptote isy=2

Step by step solution

01

Step 1. Given Information

The given function isg(x)=2x2-14x+24x2+6x-40

02

Step 2. Calculation

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

x2+6x-40=0(x-4)(x+10)=0x=4,-10

Thus, the domain of the function isx|x鈮�-10,4

03

Step 3. Calculation

Factor the numerator and denominator to make the function in lowest terms.

g(x)=2x2-14x+24x2+6x-40=2(x-4)(x-3)(x-4)(x+10)=2(x-3)(x+10)

(x+10)is the only factor in denominator so, vertical asymptote is x=-10.

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

21=2

Thus, horizontal asymptote isy=2

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