Is there a horizontal asymptote for y = 6/x - 3

[Jan Hill]

Homework Statement

would there be a horizontal asymptote for y= 6/x - 3

Homework Equations

I know that the vertical asymptote is x =3 because there the expression is undefined

The Attempt at a Solution

 

[Mark44]

Homework Statement

would there be a horizontal asymptote for y= 6/x - 3

Homework Equations

I know that the vertical asymptote is x =3 because there the expression is undefined

Yes, there is a horizontal asymptote. Any rational function in which the degree of the numerator is equal to the degree of the denominator or the degree of the numerator is less than that of the denominator always has a horizontal asymptote.

Your function can be written as y = (6 - 3x)/x, so the degrees of the numerator and denominator are equal.