: The graph of a basic rational function (1/x) is easy to do by plotting key points. When graphing rational functions, the functions are asymptotic to either the x-axis and y-axis or to certain lines if there are shifts in the graphs. More complex graphs of rational functions include functions with graph shifts.
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How to transform the graph of a rational equation up and down.
How to transform the graph of a rational equation side to side.
How to transform the graph of a rational equation upside-down.
Using transformations to graph rational functions.
Finding the discontinuities or domain restrictions of rational functions, including vertical asymptotes and holes.
How to graph rational functions using key features.
Finding x and y-intercepts of rational functions.
Finding the horizontal asymptote of a rational function and determining whether or not the graph will cross it.
Solving rational inequalities graphically
Finding discontinuities (holes and vertical asymptotes) of rational functions
Graphing rational functions using transformations.
Writing a possible rational function from given key features.