Question 10271: Graph Point for a Permitted Input

Original question and givens

In a fixed Cartesian coordinate system, D={8, 9, 10} and f:D→R is given by f(x)=(-2)x+(-1). Which ordered graph point corresponds to the permitted input 10?

• G001 — In a fixed Cartesian coordinate system, D={8, 9, 10} and f:D→R is given by f(x)=(-2)x+(-1). Which ordered graph point corresponds to the permitted input 10?

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-function-graph

Step-by-step derivation

raw domain=[8, 9, 10]

sorted distinct declared domain=[8, 9, 10]

queried expression m*x := mul(-2, 10)

queried expression m*x = -20

queried expression m*x+b := sum(-20, -1)

queried expression m*x+b = -21

x=10;declared domain=[8, 9, 10]

legal graph point=(10, -21)

Reverse checks

• S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S003 · premise_and_result_audit — Recompute queried expression m*x+b with exact rational arithmetic, not rounded decimals.
• S002 · premise_and_result_audit — Recompute queried expression m*x with exact rational arithmetic, not rounded decimals.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

(10, -21)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.