Question

Using an example, explain what the graph of a rational function looks like. Contrast this with other functions we have studied.

Answer 1

The graph of a rational function differs from that of other functions with the existence of asymptotes

Graph of rational functions

The properties of the graph of a rational function include;

• The graph of a rational function never crosses its vertical asymptote
• It crosses its horizontal or slant asymptote
• The graph of the reciprocal function y = 1/x or y = k/x is a rectangular (or right) hyperbola of which asymptotes are the coordinate axes

The graph of a rational function differs from that of other functions with the existence of asymptotes.

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