Determine the equations of the vertical and horizontal asymptotes, if any, f(x)= x/x-5

Question

Determine the equations of the vertical and horizontal asymptotes, if any, f(x)= x/x-5

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Sadie 1 week 2021-09-13T23:30:09+00:00 2 Answers 0

Answers ( )

    0
    2021-09-13T23:31:13+00:00

    Answer:

    vertical asymptote. x = 5

    horizontal asymptote, y = 1

    Step-by-step explanation:

    The vertical asymptote of f(x)= x/x-5 is gotten when the denominator x – 5 = 0 ⇒ x = 5.

    The horizontal asymptote of f(x)= x/x-5 is gotten when  we find \lim_{x \to \infty} f(x).

    So

    \lim_{x \to +\infty} f(x) = \lim_{x \to +\infty} \frac{x}{x - 5} \\= \lim_{x \to +\infty} \frac{1}{1 - \frac{5}{x} } \\= \frac{1}{1 - \frac{5}{+\infty }} \\= \frac{1}{1 - 0} \\= \frac{1}{1} \\= 1

    \lim_{x \to -\infty} f(x) = \lim_{x \to -\infty} \frac{x}{x - 5} \\= \lim_{x \to -\infty} \frac{1}{1 - \frac{5}{x} } \\= \frac{1}{1 - \frac{5}{-\infty }} \\= \frac{1}{1 + 0} \\= \frac{1}{1} \\= 1

    Since

    \lim_{n \to +\infty} f(x) = \lim_{n \to -\infty} f(x) = 1. The limit exists\\ horizontal asymptote = \lim_{n \to \infty} f(x) = 1

    0
    2021-09-13T23:31:39+00:00

    Answer: C

    Step-by-step explanation:

    EDGE 2021

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