# Question 3344: Point Value of a Continuous Affine Model

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This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth.

R0005-03344 · q-20261007-advance-20261008-r03-continuity-0019



## Original question and givens

On the whole real domain, f(x)=(19)x+(6). Find the defined point value f(3).


- G001 — On the whole real domain, f(x)=(19)x+(6). Find the defined point value f(3).





## 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-continuity](https://ocme.evemisslab.com/en/mko/mko-continuity/)





## Step-by-step derivation

S001 · impliesBefore

declared real model;center a=3

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 dependenciesRule: continuity_model_scope · Uses: G001





S002 · calculationBefore

affine slope times center := mul(19, 3)

After

affine slope times center = 57

Conditions: none

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

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S001





S003 · calculationBefore

affine center value := sum(57, 6)

After

affine center value = 63

Conditions: none

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

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S002





S004 · impliesBefore

f(x)=19x+6

After

f(3)=63

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 dependenciesRule: 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

63

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: b1117d1ca6126b2a3f119f090bc66e00766b97ce18b54f89efde8bb99ee9bc67
- candidate record SHA-256: dbd18d09395bc7479f07042365782d918fff4611b08854347f189ad5b500a019
- semantic review receipt SHA-256: 5d74de11610ebc6037a4fc9946d77154d4ed18389f8f0feeb823148b6320c4c2
- question-first witness SHA-256: 1fba4ab0f13c2cfcc4d9fdebe492c442d43dd45700394a443daa28f333355ed9
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261007-advance-20261008-r03-continuity-0019.json)