Vertical Asymptotes and Points of Discontinuity
Vertical Asymptotes Example #1
- to find the vertical asymptotes, find the values of x that make the denominator equal to 0
- set the denominator equal to 0, solve for x
- y = f(x)/(x - 3)
- x - 3 = 0
- x = 3
- y = f(x)/(x^2 + 3x - 4), factor into y = f(x)/((x - 3)(x - 1))
- (x - 3)(x - 1) = 0
- x = 3, x = 1
Vertical Asymptotes Example #2
Vertical Asymptotes Example #3
Vertical Asymptotes Example #4
Points of Discontinuity (Holes) Example #1
- if a non-permissible value of x can be cancelled out, it is a point of discontinuity (instead of being an asymptote)
- a point of discontinuity is a point missing on a graph, where it does not exist (a "hole")