SOLUTION: Determine if limx→0 f(x) exists. Is the function continuous at x = 0? f(x) = −x + 1 if x ≤ 0 2x + 3 if x

SOLUTION: Determine if limx→0 f(x) exists. Is the function continuous at x = 0? f(x) = −x + 1 if x ≤ 0 2x + 3 if x > 0 (it is a piecewise function)

Question 1133186: Determine if limx→0 f(x) exists. Is the function continuous at x = 0?
f(x) =
−x + 1 if x ≤ 0
2x + 3 if x > 0
(it is a piecewise function)
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

The limit as x approaches 0 from the left is 0+1=1; the limit as x approaches 0 from the right is 2(0)+3 = 3.

Since the limits approaching 0 from opposite sides are different, the limit as x approaches 0 does not exist, and the function is not continuous.
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