Bug introduced in 9.0 or earlier and fixed in 11.0.0
Consider this code:
f[x_]:=(6 + 4 x + x^2 - x^3)/(x-2)
Plot[f[x], {x, -10, 10},
Exclusions -> {2},
ExclusionsStyle -> Directive[Red, Dashed]]
It produces this image.

Note that the vertical exclusion is removed, but it is not styled with a red, dashed line. On the other hand, this works.
f[x_]:=(6 + 4 x + x^2 - x^3)/(x-2)
Plot[f[x], {x, -10, 10},
Exclusions -> {-2 + x == 0},
ExclusionsStyle -> Directive[Red, Dashed]]

How come?

Exclusionsneeds to return aBoolean. – David G. Stork Feb 12 '15 at 17:46Exclusions -> 2is not correct syntax. However,Exclusions -> {2}is. Both cause the exclusion to appear but none will work with styling.Exclusions -> {x==2}works with styling. This looks like a bug to me and I'm tagging it as such. Can you please report to Wolfram and let us know what they said? In the bug report I would reference theExclusions -> {2}syntax as this is clearly documented. – Szabolcs Feb 12 '15 at 18:20f[x_] = (x + 1)^2 (x - 3)/(2 - x);; however, you should includes its definition in your question. – Bob Hanlon Feb 12 '15 at 21:02Thanks for your message and for taking the time to send in the invaluable feedback. Indeed this is a wrong behaviour of Exclusions. Our developers are aware of the issue and are working to resolve it. I will keep you informed if any updates on this topic.
Thanks again for bringing the issue to our attention, most appreciated.
– David Feb 16 '15 at 17:30