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Chapter 11: Q26. (page 731)

Identify the asymptotes of each function.

y=4x2+3x鈭�28+2

Short Answer

Expert verified

The asymptotes of the given function are x=4,x=鈭�7 and y=2.

Step by step solution

01

Step 1. Define asymptotes.

A rational function which is in the form of y=ax鈭�b+c,a鈮�0 has a horizontal asymptote aty=c and a vertical asymptote at x=b.

02

Step 2. Set a denominator equal to zero.

Set a denominator of a given expression equal to zero.

x2+3x鈭�28=0

03

Step 3. Factor and simplify.

Factor the above equation and simplify further.

x鈭�4x+7=0x鈭�4=0orx+7=0x=4x=鈭�7

Therefore, the vertical asymptotes arex=4 and x=鈭�7. Horizontal asymptote is y=2.

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