Problem

Use the piecewise graph to determine its domain, range, interval behavior, function value at the junction, and continuity at the junction.

Piecewise graph with a horizontal segment from closed point 0 comma 2 to open point 3 comma 2, then a jump to closed point 3 comma 5 and an increasing segment to 6 comma 8.

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What this problem is really about

For a piecewise graph, read each segment on its own before combining the results. We’ll track the horizontal and vertical values contributed by each piece, paying special attention to open and filled markers where the rule changes. Those endpoint markers decide the actual function value at the junction and reveal whether the pieces meet continuously or make a jump.

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domain = [0,6]; range = 2∪[5,8]; decreasing = [0,3); constant = [3,6]

domain = [0,6]; range = [2,8]; constant = [0,3]; increasing = [3,6]; f(3)=2; continuity = continuous

domain = (0,6]; range = 2∪[5,8]; f(3)=2 and 5; continuity = jump

domain = [0,6]; range = 2∪[5,8]; constant = [0,3); increasing = [3,6]; f(3)=5; continuity = jump at x=3 because left-hand values approach 2 but f(3)=5

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Use the piecewise graph to determine its domain, range, interval behavior, function value at the junction, and continuity at the junction.

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