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R0019-10227 · q-20261003-r06-function-graph-0002
In a fixed Cartesian coordinate system, D={-11, -10, -9} and f:D→R is given by f(x)=(-1)x+(0). Does (-10, 11) belong to the declared graph?
G001 — In a fixed Cartesian coordinate system, D={-11, -10, -9} and f:D→R is given by f(x)=(-1)x+(0). Does (-10, 11) belong to the declared graph?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.
Before
raw domain=[-11, -10, -9]
After
sorted distinct declared domain=[-11, -10, -9]
Conditions: none
The domain is the declared finite integer subset,not automatically all R.The input list must already be distinct.The first coordinate is input,the second output.
Rule: function_graph_declared_domain_scope · Uses: G001
Before
queried expression m*x := mul(-1, -10)
After
queried expression m*x = 10
Conditions: none
Compute exactly from this step's original operands in the specified order,retaining signs and denominator conditions.
Rule: exact_rational_arithmetic · Uses: G001, S001
Before
queried expression m*x+b := sum(10, 0)
After
queried expression m*x+b = 10
Conditions: none
Compute exactly from this step's original operands in the specified order,retaining signs and denominator conditions.
Rule: exact_rational_arithmetic · Uses: G001, S002
Before
candidate point=(-10, 11);x in domain=Yes;ambient formula value=10
After
output equality=No;graph member=No
Conditions: none
The algebraic expression can have a numerical value outside D,but that is not a value of the restricted function there.Both domain membership and y=f(x) must hold.
Rule: restricted_graph_membership_two_guards · Uses: G001, S003
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.No
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
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.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 7b0263a0e9b903c22287eada7def72db184f3960f0abfbfff021e72d2b72587fcandidate record SHA-256: 729c4818c62e47ee989af53efa69f6ebb87799a20b6ceff3f81a73c601ab0ab7semantic review receipt SHA-256: eeb35dc5daab92234bf72827627392b47f38ead4cfb574d4373bebc43c09fbf5question-first witness SHA-256: 3cf8e0d3a00b0df1994db2bfde81f4a31b382e170bdda83ea3d0b68da64e8419Lean: NOT_RUN · human review: NOT_PERFORMED