Concept (1)

: 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.

Sample Problems (12)

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Graph:

 f(x) = 1 + 2 x
Problem 1
How to transform the graph of a rational equation up and down.

Graph:

 f(x) = 1 x + 3
Problem 2
How to transform the graph of a rational equation side to side.

Graph:

 f(x) = -1 x
Problem 3
How to transform the graph of a rational equation upside-down.
Problem 4
Using transformations to graph rational functions.
Problem 5
Finding the discontinuities or domain restrictions of rational functions, including vertical asymptotes and holes.
Problem 6
How to graph rational functions using key features.
Problem 7
Finding x and y-intercepts of rational functions.
Problem 8
Finding the horizontal asymptote of a rational function and determining whether or not the graph will cross it.
Problem 9
Solving rational inequalities graphically
Problem 10
Finding discontinuities (holes and vertical asymptotes) of rational functions
Problem 11
Graphing rational functions using transformations.
Problem 12
Writing a possible rational function from given key features.