Need help with Domain, Continuity, Asymptotes, and Holes?

Question

"determine the domain for eat of the following functions. state if the function is continuous or discontinuous and where any holes or asymptotes occur."

those are my instructions i'll only put one function here and ill figure the rest out on my own.

F(x) = 2x + 6

I forgot how to do this >_> thanks for the help :D

ok what about ones like this:

(5x+6)/(x^2+2)

Answer 1

x,y belong to Real

since the function is linear, no discontinuity

countinuously increasing, no asymptotes, holes when x=0, ie y=6

Answer 2

Just this example is a case of a functions that exists for all x(domain) is always continuos and has no asymptotes
so it won´t show you anything
Let´s take y =(2x^2+3)/(x^2-4)
Domain all real except x=+-2
Discont at x=2 and x= -2
The lines x=2 and x=-2 are asymptotes
lim y x==> infinity = 1 so y = 1 is also a asymptote

Answer 3

Robert has given you the incredible solutions for A), B), and C). indexed under are the solutions for D) and E) D) As x physique of techniques - 2 from above the shrink is + infinity AS x physique of techniques - 2 from under the shrink is - infinity Make up a table.... x ........f(x) .........................- a million.9 .........................- a million.ninety 9 ..........................-2.01 ...........................- 2.001 bear in mind while calculating sin x in f(x) that x is in radians. E) f is non-stop for all x < - 2, additionally for all x > - 2 different than x = 0 and x = 2.