Precalculus Textbook 8th Edition Section 1.2 Exercise 55 Solution

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Question:

Use a method of your choice to find all horizontal and vertical asymptotes of the function f(x) = x / (x – 1).

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Solution:

The given function is f(x) = x / (x – 1).

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 = 1.

Since the given function f(x) = x / (x – 1), it is undefined where denominator (x – 1) is zero.

Then, x – 1 = 0, Then x = 1

Thus, the vertical asymptote of the given function is x = 1.

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