Problem preview
F-IF.7.b Warmup M3-024-A09-V01

Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions.

Evaluate a piecewise-defined function at its boundary value

Problem

Use the displayed piecewise definition and graph to find \(f(2)\).

Big Picture

What this problem is really about

At a piecewise boundary, evaluate the conditions before evaluating either formula. The rule whose inequality includes equality owns the boundary input; the other rule only describes nearby values from its side. The closed and open points on the graph should confirm that same ownership, so use them as a consistency check rather than a separate rule.

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Four variants of this problem type
Curriculum context
Course
Math III
Standard
F-IF.7.b
Category
Functions
Domain
Interpreting Functions
Objective
Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions.
Problem type
Evaluate a piecewise-defined function at its boundary value