Question

Graph the piecewise function f(x)={x+5 if x≤−22x+3 if x>−2 . Will the graph have any open endpoints? If yes, where?(1 point)
Responses

Yes, at (−2,3) .
Yes, at left parenthesis negative 2 comma 3 right parenthesis .

Yes, at (−2,−1) .
Yes, at left parenthesis negative 2 comma negative 1 right parenthesis .

No, all endpoints are closed.
No, all endpoints are closed.

Yes, at (−2,3) and (−2,−1) .
Yes, at left parenthesis negative 2 comma 3 right parenthesis and left parenthesis negative 2 comma negative 1 right parenthesis .

Answer 1

Yes — at (-2, -1).

Reason: For x ≤ -2 the value is x+5, so the point (-2, 3) is included (closed). For x > -2 the value is 2x+3, so the right-hand branch would give (-2, -1) but x = -2 is excluded, so that endpoint is open.