Question 10210: Listing a Finite Function Graph

Original question and givens

In a fixed Cartesian coordinate system, D={-3, -2, -1} and f:D→R is given by f(x)=(2)x+(0). List the complete graph in increasing order of first coordinate, listing identical points once.

• G001 — In a fixed Cartesian coordinate system, D={-3, -2, -1} and f:D→R is given by f(x)=(2)x+(0). List the complete graph in increasing order of first coordinate, listing identical points once.

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=[-3, -2, -1]

sorted distinct declared domain=[-3, -2, -1]

domain input-3 m*x := mul(2, -3)

domain input-3 m*x = -6

domain input-3 m*x+b := sum(-6, 0)

domain input-3 m*x+b = -6

legal input=-3;formula value=-6

graph point=(-3, -6)

domain input-2 m*x := mul(2, -2)

domain input-2 m*x = -4

domain input-2 m*x+b := sum(-4, 0)

domain input-2 m*x+b = -4

legal input=-2;formula value=-4

graph point=(-2, -4)

domain input-1 m*x := mul(2, -1)

domain input-1 m*x = -2

domain input-1 m*x+b := sum(-2, 0)

domain input-1 m*x+b = -2

legal input=-1;formula value=-2

graph point=(-1, -2)

complete legal-input points=[[-3, -6], [-2, -4], [-1, -2]]

finite graph={(-3, -6), (-2, -4), (-1, -2)}

Reverse checks

• S011 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S010 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S009 · premise_and_result_audit — Recompute domain input-1 m*x+b with exact rational arithmetic, not rounded decimals.
• S008 · premise_and_result_audit — Recompute domain input-1 m*x with exact rational arithmetic, not rounded decimals.
• S007 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S006 · premise_and_result_audit — Recompute domain input-2 m*x+b with exact rational arithmetic, not rounded decimals.
• S005 · premise_and_result_audit — Recompute domain input-2 m*x with exact rational arithmetic, not rounded decimals.
• 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 domain input-3 m*x+b with exact rational arithmetic, not rounded decimals.
• S002 · premise_and_result_audit — Recompute domain input-3 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

{(-3, -6), (-2, -4), (-1, -2)}

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.