Question

Will the graph of the function f(x)={−x−3 if x≤−4−2 if x>−4
be continuous? Why or why not?(1 point)

No, because there will be a gap in the graph.

No, because the horizontal line is not considered continuous.

Yes, because the pieces of the function use the same value as the change point.

Yes, because the slopes of all the pieces are the same.

Answer 1

No — because the left-hand value at x = −4 is f(−4) = −(−4) − 3 = 1 while the right-hand limit is −2, so the values don't match and there's a jump (gap) at x = −4. Hence option 1.