Question

How do I identify the horizontal asymptotes of `f(x) = (4x)/7`?

Answer 1

This function does not have any horizontal asymptotes. This function is in slope intercept form, `y=mx+b`.

It's a linear function, just a line, with a slope of `4/7` and a y-intercept of 0 because `b=0`.

Asymptote rules:

If the degree of the numerator is less than the degree of the denominator then the x-axis is the horizontal asymptote.

If the numerator and denominator have the same degree then the quotient of those coefficients is the horizontal asymptote.

If the degree of the numerator is greater than the degree of the denominator then there is no horizontal asymptote.

In this example the degree of the numerator is `1` and the degree of the denominator is `0`. `1 > 0` so we do not have any horizontal asymptotes.