Question

Suppose
g(x) = { 1 / (x-2) if x < 1
2x - 3 if x >/= 1
The best description concerning the continuity of g(x) is that the function
A.) is continuous
B.) has a jump discontuity
C.) has an infinite discontuity
D.) has a removable discontuity
E.) None of the above

Answer 1

Sorry, it should be "Discontinuity."

Answer 2

1. Find out if there is any vertical asymptote in each respective domain, i.e. if a vertical asymptote exists for 1/(x-2) at x<1, and if one exists for 2x-3 at x≥1.
2. If there is any, then g(x) is discontinuous.
Otherwise check if it is continuous at x=1, i.e. if the limit x->1- equals the limit x->1+.
3. If 2 is satisfied, verify if g(1) exists.
If it exists, g(x) is continuous in the interval (-∞,+∞).

Answer 3

Suppose g(x) = { 1 / (x-2) if x < 1
{2x - 3 if x >/= 1
The best description concerning the continuity of g(x) is that the function
A.) is continuous
B.) has a jump discontuity
C.) has an infinite discontuity
D.) has a removable discontuity
E.) None of the above