are there any asymptotes on an absolute value function? ((at the cusp?))
i have function |x^2-6x+5|
it has zeros at 5, 1 --> i wouldnt say that there are vertical asymptotes there, right? because it is defined there?
2006-11-22 05:48:51 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
why would there be a h.a. at y=3? the function goes through that. that isnt right.
2006-11-22 05:59:32 · update #1
There are no asymptotes in this graph. y=3 is not an asymptote but the tangent to the curve at the local maximum.
The only thing interesting happening at x=1 and x=5, besides being roots and local minimums is that the first and second derivatives are not continuous at those points. However, the limits of the derivatives exist coming to 1 and 5 from left and right.
2006-11-22 10:13:24 · answer #1 · answered by Dr. J. 6 · 0⤊ 0⤋
You are correct; an asymptote is a line that a graph approaches as its variable gets large (or small) but never actually reaches. This graph has none at all.
2006-11-22 13:58:58 · answer #2 · answered by hayharbr 7 · 0⤊ 0⤋
HA: y=3
there is no vertical asymptotes because the denominator is 1
2006-11-22 13:53:07 · answer #3 · answered by 7 · 0⤊ 1⤋
Correct, veriticle asymtotes only occur in division
2006-11-22 13:53:34 · answer #4 · answered by TheTechKid 3 · 0⤊ 1⤋
At the cusp, -infinity and + infinity
2006-11-22 13:54:23 · answer #5 · answered by kellenraid 6 · 0⤊ 0⤋