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R0019-10201 · q-20261003-r06-function-graph-0051
In a fixed Cartesian coordinate system, D=∅ and f:D→R is given by f(x)=(-2)x+(-1). List the complete graph in increasing order of first coordinate, listing identical points once.
G001 — In a fixed Cartesian coordinate system, D=∅ and f:D→R is given by f(x)=(-2)x+(-1). List the complete graph in increasing order of first coordinate, listing identical points once.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=[]
After
sorted distinct declared domain=[]
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
complete legal-input points=[]
After
finite graph=∅
Conditions: none
List the complete set in increasing first-coordinate order.An empty domain gives∅,not an invented(0,0).
Rule: complete_finite_graph_set · Uses: G001, S001
S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.∅
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: b15e00f29074a9839f44d10bb91ac7c16d3fe57c12ccd7a586a8d7ae6cf47dd7candidate record SHA-256: 1babaa05031908ff50f74357c4985b86687509d27bc32276abfc22cc86e9135dsemantic review receipt SHA-256: eeb35dc5daab92234bf72827627392b47f38ead4cfb574d4373bebc43c09fbf5question-first witness SHA-256: 3cf8e0d3a00b0df1994db2bfde81f4a31b382e170bdda83ea3d0b68da64e8419Lean: NOT_RUN · human review: NOT_PERFORMED