Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions, showing key features by hand in simple cases and with technology when the functions are more complicated.
Specify a step graph with exact boundary ownership
Problem
Create the exact graph record for \(f(x)=2\) on \([0,3)\) and \(f(x)=5\) on \([3,6)\). Specify each horizontal segment with open or closed endpoints, determine interval ownership at \(x=3\) and therefore \(f(3)\), and state the complete domain and range.
A step graph is defined as much by endpoint ownership as by the heights of its horizontal pieces. We’ll translate each interval bracket into an open or closed marker, make sure the shared boundary belongs to exactly one step, and combine the covered inputs and attained levels into the domain and range.
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