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Question 3329: Point Value of a Continuous Affine Model

On this page
  1. Original question and givens
  2. Definition and scope
  3. Step-by-step derivation
  4. Reverse checks
  5. Result
  6. This question review and source binding

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R0005-03329 · q-20261007-advance-20261008-r03-continuity-0004

Original question and givens

On the whole real domain, f(x)=(-4)x+(-9). Find the defined point value f(4).

  • G001 — On the whole real domain, f(x)=(-4)x+(-9). Find the defined point value f(4).

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.

Step-by-step derivation

S001 · implies

Before

declared real model;center a=4

After

distinguish punctured limits,point values and a new extension

Conditions: none

Use the declared real formulas;point values,punctured limits and values of a newly defined extension are different data.

Step identifiers and dependencies

Rule: continuity_model_scope · Uses: G001

S002 · calculation

Before

affine slope times center := mul(-4, 4)

After

affine slope times center = -16

Conditions: none

Substitute the center a into this affine formula's product term.

Step identifiers and dependencies

Rule: exact_rational_arithmetic · Uses: G001, S001

S003 · calculation

Before

affine center value := sum(-16, -9)

After

affine center value = -25

Conditions: none

Then add this branch's intercept,not the other branch's constant.

Step identifiers and dependencies

Rule: exact_rational_arithmetic · Uses: G001, S002

S004 · implies

Before

f(x)=-4x+-9

After

f(4)=-25

Conditions: none

This task evaluates the declared affine model at one point;a single reading does not prove continuity of an arbitrary function.

Step identifiers and dependencies

Rule: affine_point_evaluation_only · Uses: G001, S003

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 affine center value with exact rational arithmetic, not rounded decimals.
  • S002 · premise_and_result_audit — Recompute affine slope times center 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

-25

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.

Source hashes and review receipts
  • input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
  • original question SHA-256: a1ff49bd6d8c06de7f0c2bd22a7397a2a1af17817c9f482ea5ca504135867ab9
  • candidate record SHA-256: f59a788a3c9301b3675ae41197a2982f38c7ab0768c0469204eaf9996acb69d1
  • semantic review receipt SHA-256: 5d74de11610ebc6037a4fc9946d77154d4ed18389f8f0feeb823148b6320c4c2
  • question-first witness SHA-256: 1fba4ab0f13c2cfcc4d9fdebe492c442d43dd45700394a443daa28f333355ed9
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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