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Vertical Asymptotes of Rational Functions

Question 12 • (OC27) MATH COLL ALGEBRA-1200710-S1-Degele-VOL7006P

Sound intensity, I, from a spherical source is a function of the distance, r, from the source of the sound. It is represented by the functionwhere P is the power of the sound. Explain the behavior of the graph of I and what it means in context.

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Answer:

The function I = P / (4πr²) is a rational function. It has a vertical asymptote at r = 0, which means the sound intensity is undefined at the source. It also has a horizontal asymptote at I = 0, indicating that as the distance (r) from the sound source increases, the intensity (I) decreases and approaches zero.

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