Question

The graph of a rational function never intersects a _______ asymptote.

Short answer

The graph of a rational function never intersects a vertical asymptote.

Step-by-step solution

Step 1 Definition for the asymptote:

An asymptote is a straight line that continually approaches a given curve but does not meet it at any finite distance.

They are of three types. They are,

1. Horizontal asymptote.
2. Vertical asymptote.
3. Oblique asymptote.

Step 2 The graph of a rational function never intersects a vertical asymptote.

This is because, the vertical asymptotes are the vertical lines which corresponds to the zeros of the denominator of the rational function. At zeros of the denominator the rational function will always have undefined value and hence the graph of a rational function never intersects a vertical asymptote.