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?
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
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!