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.
Evaluate a piecewise-defined function at a given x-value
Problem
Evaluate piecewise function \(f(x)=x+1\) for \(x<2\); \(f(x)=5\) for \(x\ge~2\) at \(x=2\).
Big Picture
What this problem is really about
Evaluating a piecewise function begins with interval membership, not substitution. We’ll test the target input against the conditions, use the inclusive or strict boundary symbol to identify exactly one rule, and then evaluate only that active piece.
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