Precalculus Textbook 8th Edition Section 2.6 Exercise 19 Solution

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Question:

Find the Horizontal and Vertical asymptotes of the function f(x) = (2x² – 1) / (x² + 3). Use the limits to describe the corresponding behavior.

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Solution:

Given polynomial is f(x) = (2x² – 1) / (x² + 3)

Horizontal asymptote of a function is line y = k where k = Value of f(x) at x tends to infinity.

Vertical asymptote of a function is line x = t where t = Values of x at which function f(x) is undefined.

Now,

Thus, the horizontal asymptote of the given function is y = 2.

Hence, the end behaviors of the given function are .

Since the given function f(x) = (2x² – 1) / (x² + 3), it is defined everywhere as its denominator (x² + 3)

is non-zero for any real value of x.

Thus, there is NO vertical asymptote of the given function.

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