Describe the continuity of the function f(x) = (x^2-16)/(x^2-9x+20). For each point of discontinuity, describe the graph's behavior in terms of asymptotes, removable discontinuities, etc.

Question

jmartinez638 · Answer

$$f(x) = \frac{x^{2}-16 }{x^{2}-9x+20}$$

anonymous · Answer

factor both the numerator and denominator.
Anything that cancels out is a hole (removable discontinuity).
From what's left after canceling, set the denominator equal to 0 to find the vertical asymptotes (infinite discontinuity)

jmartinez638 · Answer

Ok, I'll do that. Thanks!

jmartinez638 · Answer

Removable discontinuity at x-4, and vertical asymptote at x+5

anonymous · Answer

x - 4 = 0
x = 4
so removable disc. @ x = 4

x - 5 = 0
x = 5
vertical asymptote is x = 5