Question

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

Answer 1

Answer: C

Explanation:

EDGE 2021

Answer 2

vertical asymptote. x = 5

horizontal asymptote, y = 1

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) (x)/(x - 5) \\= \lim_(x \to +\infty) (1)/(1 - (5)/(x) ) \\= (1)/(1 - (5)/(+\infty )) \\= (1)/(1 - 0) \\= (1)/(1) \\= 1`

`\lim_(x \to -\infty) f(x) = \lim_(x \to -\infty) (x)/(x - 5) \\= \lim_(x \to -\infty) (1)/(1 - (5)/(x) ) \\= (1)/(1 - (5)/(-\infty )) \\= (1)/(1 + 0) \\= (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`