is the following function continuous at x=3 ? f(x)= { x-2 if x< or = 3 , 2-x if x>3?

Answer 1

x≤ 3:

f(x)=x-2
f(3)=3-2 = 1

x>3:
f(x)=2-x
f(3)=2-3 = -1 ≠ 1 = 3-2 = f(3)

Answer: the function is not continuous at x=3

₢

Answer 2

No. When x <=3, the function is y = x - 2. At x=3, the function = 1. But it immediately jumps to -1 and continues with y = -x + 2 for any value > 3.