Which one of the following functions is continuous at x = 3?

A. f(x) = { 2, if x = 3
{ x - 1, if x != 3...

Question

Which one of the following functions is continuous at x = 3?

A. f(x) = { 2,      if x = 3
           { x - 1, if x != 3

B. f(x) = { 4,      if x = 3
           { 8/(x-3), if x != 3

C. f(x) = { x + 3, if x <= 3
           { x - 4, if x != 3

D. f(x) = { 1/(x-3), if x != 3

Accepted Answer

Option A is continuous at x = 3. Answer: A. For f to be continuous at x = 3, three things must hold: f(3) is defined, the limit as x approaches 3 exists, and that limit equals f(3). We check the limit value of each option and compare it to the given f(3). Most options have a mismatch or an undefined limit; option A has lim_{x->3}(x-1) = 2 which equals f(3) = 2.

Which one of the following functions is continuous at x = 3? A. f(x) = { 2, if x = 3 { x - 1, if x != 3 B. f(x) = { 4, if x = 3 { 8/(x-3), if x != 3 C. f(x) = { x + 3, if x <= 3 { x - 4, if x != 3 D. f(x) = { 1/(x-3), if x != 3