STEM REASONING AND EVIDENCE WORKBENCH
Select the correct side of one boundary, evaluate a two-piece linear function, and audit learner endpoint values.
Review output
Load the worked example to inspect realistic inputs, or enter anonymous classroom or laboratory evidence. Results remain in this browser tab until you copy or download them.
Transparent method
First compare x with the boundary. Select the left rule when x is smaller, or when x equals the boundary and left-inclusive is yes; otherwise select the right rule. Evaluate only that rule as slope times x plus intercept. The unselected expression does not contribute to the value. A supported row agrees with the interval decision and arithmetic. A boundary conflict suggests checking inequality symbols and open or closed points before reteaching substitution. A correct value away from the boundary does not prove endpoint understanding, so inspect a boundary item and ask the learner to name the condition before calculating.
Confirm the question, approved source, units, notation, signs, response coding, model assumptions, and review threshold. Keep an unchanged copy of measurements or learner evidence.
Run the worked example, inspect every intermediate row, and compare the result with a hand calculation, diagram, representation, periodic table, or approved laboratory method.
Record the method, assumptions, uncertainty, units, classifications, and flagged rows. Verify the editable report independently before instruction, assessment, or laboratory use.
How to interpret the result
Use when learners must read interval conditions before substituting into a formula, especially at an open or closed endpoint. The diagnostic supports exactly two linear pieces around one boundary. It does not parse free-form notation, graph discontinuities automatically, solve inverse problems, handle several intervals, or infer a misconception from one response.
With boundary two and the left rule 3x plus 1, x equals one gives four and an included x equals two gives seven. The right rule negative x plus eight gives three at x equals five. When equality instead belongs to the right rule, the boundary value is six, so a repeated answer of seven is flagged.
First compare x with the boundary. Select the left rule when x is smaller, or when x equals the boundary and left-inclusive is yes; otherwise select the right rule. Evaluate only that rule as slope times x plus intercept. The unselected expression does not contribute to the value.
A supported row agrees with the interval decision and arithmetic. A boundary conflict suggests checking inequality symbols and open or closed points before reteaching substitution. A correct value away from the boundary does not prove endpoint understanding, so inspect a boundary item and ask the learner to name the condition before calculating.
Do not evaluate both formulas and choose a convenient answer, ignore equality, treat an open point as included, substitute the boundary instead of x, or assume the graph is continuous. Mark the interval first, circle the selected rule, keep signs and parentheses visible, and compare the result with the graph.
Learning boundary
This browser-local workbench applies only the disclosed rules. It cannot diagnose a learner, certify an experiment, establish a chemical structure, or replace teacher, laboratory, and safety judgment.
Review checklist
Practical questions
No. Processing occurs in the current browser tab. Avoid personal information and retain authoritative records only in the school-approved system.
No. It describes entered evidence under one disclosed rule. Compare several evidence sources and ask for reasoning before drawing a conclusion.
Treat it as an editable calculation aid. Show your own reasoning, cite required sources, and follow the course method and academic-integrity rules.
YOUR NIRMION
