Asymptote problem?

Question

Vertical asy, horizontal asy, and any removable discontinuities

y= (5x+1) / (x^2-x-1)

Cannot seem to get this one....

Answer 1

The rationa lfunction

Vertical asymptotes are found  by solving denominator = 0

Compare it to

Roots are

To find horizontal asymptote.

Degree of the numarator = 1 and the degree of denominator = 2.

If the degree of the numerator is less than the degree of the denominator, the line

y = 0 (x - axis) is the horizontal asymptote.

The given function is not defined at x = − 0.61 and x = 1.61.

This function has  removable discontinuities at x = − 0.61 and x = 1.61.

 

Comments

Sorry, look at the graph of the function. The discontinuities are not removable.  At the discontinuities the limit from one side is postive infinity and from the other side negative infinity.  Never the twain shall meet.