Thread: location of asymptotes and points of discontinuity

2x+5
_______
(x-1)(x+5)

Determine the location of asymptotes and points of discontinuity if they exist.

I know how to solve it with graphing but how do I find it without graphing?

Originally Posted by power2600

2x+5
_______
(x-1)(x+5)

Determine the location of asymptotes and points of discontinuity if they exist.
I know how to solve it with graphing but how do I find it without graphing?

Hello,

I assume that you should examine the function:

Code:

         2x+5
f(x) = ----------
       (x-1)(x+5)

1. Calculate the domain of f: d = IR \ {-5, 1} because the denominator must be unequal to zero. The equations x = -5 and x = 1 describe the vertical asymptotes

2.

Code:

         2x+5
f(x) = -----------
       x² + 4x - 5

The degree ofthe numerator is smaller than the degree of the denominator therefore f has a horizontal asymptote: y = 0 (or in other words: The x-axis is a sysmptote of f)

I've attached a diagram of the function.