# How do you find the x- and y-intercepts of #f(x) = (4 - x) / x#, then determine whether the graph of f touches or crosses the x-axis at the x-intercept?

##### 1 Answer

Let's start by determining the

There is no y-intercept, since there is an asymptote at

For the x-intercept:

To determine the behaviour of the graph at the *horizontal asymptote*.

Since the degree of the numerator equals the degree of the denominator, the horizontal asymptote will occur at the ratio between the coefficients of the highest degree in the numerator and denominator.

This would be

So, the horizontal asymptote is at

Hopefully this helps!