Suppose

Question

g(x) = { 1 / (x - 2) if x < 1
2x - 4 if x >/= 1
The best description concerning the continuity of g(x) is that the function
A.) is continuous
B.) has a jump discontinuity
C.) has an infinite discontinuity
D.) has a removable discontinuity
E.) None of the above

Answer 1

notice that as x--> 1
g(1) --> 1/(1-2) = -1

but g(1) from the second function is 2(1) - 4 = -2

so there is a "jump" from -1 to -2 in the value of g(x)
in the transition at x = 1

Does that help?
Did you sketch it?
The following page let's you graph several different functions on the same grid
http://rechneronline.de/function-graphs/