In this lesson (8.3,4,5) we started graphing and understanding reciprocal functions of linear and quadratic equations.

Reciprocal linear functions:

Reciprocals of linear functions will always create a “2 part graph” this is referred to as a hyperbola, a hyperbola of a linear graph will always have two “swooping L” shaped lines exactly opposite each other in opposite quadrants of the graph. Ex. Located in top left and bottom right quadrant.

Reciprocal quadratic functions:

Reciprocals of quadratic functions, similarly to linear functions will also create a hyperbola, however it may sometimes look slightly different, for example you may have two “swooping L’s” each on the same side of the graph (positive or negative), you may even have a third section on your graph if the parabola dips below the X axis and into the negative section of the graph. Reciprocal graphs of quadratic functions may even yield 2 or three asymptotes and as many as 4 invariant points.

New vocabulary:

critical points- the point upon which the line on the graph abruptly changes direction

invariant points- 1, and -1, points that remain the same when’s reciprocated

asymptotes- invisible lines that cross the x and y intercepts And “reorganize/separate” sections of the graph, these are the undefined values.