Inside Collection (Course): "Rational"ity

Summary: Finding discontinuities - vertical asymptotes and holes - of rational functions

Vertical Asymptotes occur when factors in the denominator = 0 and do not cancel with factors in the numerator

- Vertical asymptotes are vertical lines the graph approaches
- The equation of the vertical asymptote is x = (that number which makes the denominator = 0)

- Holes are open "points" so they have an x and y coordinate
- The x-value is the number that makes the cancelled factor = 0.
- The y-value is found by substituting x into the "reduced" equation (
*after*cancelling) like factors.

Find the vertical asymptotes and holes (if any) for the following. Don't forget that vertical asymptotes are equations and holes are points!

Vertical Asymptote:

Hole: None

Vertical Asymptote: None

Hole: (1,1) since (x-1) was cancelled, the hole is at x=1. To find the y-coordinate, plug 1 into the reduced equation:

Vertical Asymptote:

Hole: None

Vertical Asymptote:

Hole: None

Vertical Asymptote:

Hole: None

Vertical Asymptote:

Hole: None

Vertical Asymptote:

Hole: None

Vertical Asymptote: None since

Hole: None

Vertical Asymptote: None since

Hole: None

Vertical Asymptote:

Hole: None

Vertical asymptotes:

Hole: None

Vertical Asymptote:

Hole: (3,

Vertical Asymptote:

Hole: None since the vertical asymptote takes care of the hole.

Vertical Asymptote: None

Hole: (-2,-4) since

Vertical Asymptotes: None

Holes: (3,3), (0,0) since

Vertical Asymptote: None

Hole: (1,3) since

Vertical asymptote:

Hole: (-1,

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