Where are the asymptotes for the following function located? f (x) = StartFraction 14 Over (x minus 5) (x + 1) EndFraction

recall that asymptotic occur at the locations that will make the equation undefined. In this case, the asymptote will occur at x-locations which will cause the denominator to become zero (and hence undefined)

Equating the denominator to zero,

(x-5)(x+1) = 0

(x-5) =0

x = 5 (first asymptote)

or (x+1) = 0

x = -1 (2nd asymptote)

facundo3141592 facundo3141592 · Answer 2 · 2021-11-12T13:48:08+01:00

We want to find the asymptotes of the given function.

There are two vertical asymptotes, one at x =5 and the other at x = -1.

First, we can briefly describe what an asymptote is.

An asymptote is a tendency to a given value that never reaches the actual value.

For example, we have vertical asymptotes (that tend to infinity or negative infinity) when we have a quotient with a denominator equal to zero.

Then, for our function:

[tex]f(x) = \frac{14}{(x-5)*(x +1)}[/tex]

We need to find the values of x such that the denominator becomes zero.

Is ratter easy to see that if x = 5, or x = -1, the denominator becomes equal to zero, then we will have two vertical asymptotes, one at x = 5 and other at x = -1.

If you want to learn more, you can read:

https://brainly.com/question/4084552