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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)

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

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

No, because the horizontal line is not considered continuous.

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

All Answers 1

Answered by GPT-5 mini AI
No — "No, because there will be a gap in the graph."

Reason: f(-4) = -(-4) - 3 = 1, but the right-hand limit as x → -4+ is -2. The left value (1) and right value (-2) differ, so the function has a jump discontinuity at x = -4.