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This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.
batch-20260930-r03-domain-codomain-range-foundations · 2026-09-30 · 100 questions
This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.
Given the explicit declaration A=∅, B={-2, 0, 3}, ordered pairs=[] and a total function f:A→B, list the domain in increasing order.
∅
The domain is the explicitly declared input set A=∅; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A=∅, B=∅, ordered pairs=[] and a total function f:A→B, list the domain in increasing order.
∅
The domain is the explicitly declared input set A=∅; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A={-10, -9, -8, -7}, B={-4, 0, 5}, ordered pairs=[(-10, 5), (-9, -4), (-8, 0), (-7, 5)] and a total function f:A→B, list the domain in increasing order.
{-10, -9, -8, -7}
The domain is the explicitly declared input set A={-10, -9, -8, -7}; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A={-9, -8}, B={-6, 0, 7}, ordered pairs=[(-9, -6), (-8, 0)] and a total function f:A→B, list the domain in increasing order.
{-9, -8}
The domain is the explicitly declared input set A={-9, -8}; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A={-8, -7, -6}, B={-8, 0, 9}, ordered pairs=[(-8, 0), (-7, 9), (-6, -8)] and a total function f:A→B, list the domain in increasing order.
{-8, -7, -6}
The domain is the explicitly declared input set A={-8, -7, -6}; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A={-7, -6, -5, -4}, B={-10, 0, 11}, ordered pairs=[(-7, 11), (-6, -10), (-5, 0), (-4, 11)] and a total function f:A→B, list the domain in increasing order.
{-7, -6, -5, -4}
The domain is the explicitly declared input set A={-7, -6, -5, -4}; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A={-6, -5}, B={-12, 0, 13}, ordered pairs=[(-6, -12), (-5, 0)] and a total function f:A→B, list the domain in increasing order.
{-6, -5}
The domain is the explicitly declared input set A={-6, -5}; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A={-5, -4, -3}, B={-14, 0, 15}, ordered pairs=[(-5, 0), (-4, 15), (-3, -14)] and a total function f:A→B, list the domain in increasing order.
{-5, -4, -3}
The domain is the explicitly declared input set A={-5, -4, -3}; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A={-4, -3, -2, -1}, B={-16, 0, 17}, ordered pairs=[(-4, 17), (-3, -16), (-2, 0), (-1, 17)] and a total function f:A→B, list the domain in increasing order.
{-4, -3, -2, -1}
The domain is the explicitly declared input set A={-4, -3, -2, -1}; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A={-3, -2}, B={-18, 0, 19}, ordered pairs=[(-3, -18), (-2, 0)] and a total function f:A→B, list the domain in increasing order.
{-3, -2}
The domain is the explicitly declared input set A={-3, -2}; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A={-2, -1, 0}, B={-20, 0, 21}, ordered pairs=[(-2, 0), (-1, 21), (0, -20)] and a total function f:A→B, list the domain in increasing order.
{-2, -1, 0}
The domain is the explicitly declared input set A={-2, -1, 0}; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A={-1, 0, 1, 2}, B={-22, 0, 23}, ordered pairs=[(-1, 23), (0, -22), (1, 0), (2, 23)] and a total function f:A→B, list the domain in increasing order.
{-1, 0, 1, 2}
The domain is the explicitly declared input set A={-1, 0, 1, 2}; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A={0, 1}, B={-24, 0, 25}, ordered pairs=[(0, -24), (1, 0)] and a total function f:A→B, list the domain in increasing order.
{0, 1}
The domain is the explicitly declared input set A={0, 1}; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A={1, 2, 3}, B={-26, 0, 27}, ordered pairs=[(1, 0), (2, 27), (3, -26)] and a total function f:A→B, list the domain in increasing order.
{1, 2, 3}
The domain is the explicitly declared input set A={1, 2, 3}; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A={2, 3, 4, 5}, B={-28, 0, 29}, ordered pairs=[(2, 29), (3, -28), (4, 0), (5, 29)] and a total function f:A→B, list the domain in increasing order.
{2, 3, 4, 5}
The domain is the explicitly declared input set A={2, 3, 4, 5}; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A={3, 4}, B={-30, 0, 31}, ordered pairs=[(3, -30), (4, 0)] and a total function f:A→B, list the domain in increasing order.
{3, 4}
The domain is the explicitly declared input set A={3, 4}; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A={4, 5, 6}, B={-32, 0, 33}, ordered pairs=[(4, 0), (5, 33), (6, -32)] and a total function f:A→B, list the domain in increasing order.
{4, 5, 6}
The domain is the explicitly declared input set A={4, 5, 6}; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A={5, 6, 7, 8}, B={-34, 0, 35}, ordered pairs=[(5, 35), (6, -34), (7, 0), (8, 35)] and a total function f:A→B, list the domain in increasing order.
{5, 6, 7, 8}
The domain is the explicitly declared input set A={5, 6, 7, 8}; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A={6, 7}, B={-36, 0, 37}, ordered pairs=[(6, -36), (7, 0)] and a total function f:A→B, list the domain in increasing order.
{6, 7}
The domain is the explicitly declared input set A={6, 7}; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A={7, 8, 9}, B={-38, 0, 39}, ordered pairs=[(7, 0), (8, 39), (9, -38)] and a total function f:A→B, list the domain in increasing order.
{7, 8, 9}
The domain is the explicitly declared input set A={7, 8, 9}; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A={8, 9, 10, 11}, B={-40, 0, 41}, ordered pairs=[(8, 41), (9, -40), (10, 0), (11, 41)] and a total function f:A→B, list the domain in increasing order.
{8, 9, 10, 11}
The domain is the explicitly declared input set A={8, 9, 10, 11}; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A={9, 10}, B={-42, 0, 43}, ordered pairs=[(9, -42), (10, 0)] and a total function f:A→B, list the domain in increasing order.
{9, 10}
The domain is the explicitly declared input set A={9, 10}; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A={10, 11, 12}, B={-44, 0, 45}, ordered pairs=[(10, 0), (11, 45), (12, -44)] and a total function f:A→B, list the domain in increasing order.
{10, 11, 12}
The domain is the explicitly declared input set A={10, 11, 12}; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A={11, 12, 13, 14}, B={-46, 0, 47}, ordered pairs=[(11, 47), (12, -46), (13, 0), (14, 47)] and a total function f:A→B, list the domain in increasing order.
{11, 12, 13, 14}
The domain is the explicitly declared input set A={11, 12, 13, 14}; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A={12, 13}, B={-48, 0, 49}, ordered pairs=[(12, -48), (13, 0)] and a total function f:A→B, list the domain in increasing order.
{12, 13}
The domain is the explicitly declared input set A={12, 13}; it is not inferred from the outputs.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-domain-set · candidate
Given the explicit declaration A=∅, B={-2, 0, 3}, ordered pairs=[] and a total function f:A→B, list the codomain in increasing order.
{-2, 0, 3}
The codomain is the explicitly declared output set B={-2, 0, 3}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A=∅, B=∅, ordered pairs=[] and a total function f:A→B, list the codomain in increasing order.
∅
The codomain is the explicitly declared output set B=∅; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A={-10, -9, -8, -7}, B={-4, 0, 5}, ordered pairs=[(-10, 5), (-9, -4), (-8, 0), (-7, 5)] and a total function f:A→B, list the codomain in increasing order.
{-4, 0, 5}
The codomain is the explicitly declared output set B={-4, 0, 5}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A={-9, -8}, B={-6, 0, 7}, ordered pairs=[(-9, -6), (-8, 0)] and a total function f:A→B, list the codomain in increasing order.
{-6, 0, 7}
The codomain is the explicitly declared output set B={-6, 0, 7}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A={-8, -7, -6}, B={-8, 0, 9}, ordered pairs=[(-8, 0), (-7, 9), (-6, -8)] and a total function f:A→B, list the codomain in increasing order.
{-8, 0, 9}
The codomain is the explicitly declared output set B={-8, 0, 9}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A={-7, -6, -5, -4}, B={-10, 0, 11}, ordered pairs=[(-7, 11), (-6, -10), (-5, 0), (-4, 11)] and a total function f:A→B, list the codomain in increasing order.
{-10, 0, 11}
The codomain is the explicitly declared output set B={-10, 0, 11}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A={-6, -5}, B={-12, 0, 13}, ordered pairs=[(-6, -12), (-5, 0)] and a total function f:A→B, list the codomain in increasing order.
{-12, 0, 13}
The codomain is the explicitly declared output set B={-12, 0, 13}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A={-5, -4, -3}, B={-14, 0, 15}, ordered pairs=[(-5, 0), (-4, 15), (-3, -14)] and a total function f:A→B, list the codomain in increasing order.
{-14, 0, 15}
The codomain is the explicitly declared output set B={-14, 0, 15}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A={-4, -3, -2, -1}, B={-16, 0, 17}, ordered pairs=[(-4, 17), (-3, -16), (-2, 0), (-1, 17)] and a total function f:A→B, list the codomain in increasing order.
{-16, 0, 17}
The codomain is the explicitly declared output set B={-16, 0, 17}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A={-3, -2}, B={-18, 0, 19}, ordered pairs=[(-3, -18), (-2, 0)] and a total function f:A→B, list the codomain in increasing order.
{-18, 0, 19}
The codomain is the explicitly declared output set B={-18, 0, 19}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A={-2, -1, 0}, B={-20, 0, 21}, ordered pairs=[(-2, 0), (-1, 21), (0, -20)] and a total function f:A→B, list the codomain in increasing order.
{-20, 0, 21}
The codomain is the explicitly declared output set B={-20, 0, 21}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A={-1, 0, 1, 2}, B={-22, 0, 23}, ordered pairs=[(-1, 23), (0, -22), (1, 0), (2, 23)] and a total function f:A→B, list the codomain in increasing order.
{-22, 0, 23}
The codomain is the explicitly declared output set B={-22, 0, 23}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A={0, 1}, B={-24, 0, 25}, ordered pairs=[(0, -24), (1, 0)] and a total function f:A→B, list the codomain in increasing order.
{-24, 0, 25}
The codomain is the explicitly declared output set B={-24, 0, 25}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A={1, 2, 3}, B={-26, 0, 27}, ordered pairs=[(1, 0), (2, 27), (3, -26)] and a total function f:A→B, list the codomain in increasing order.
{-26, 0, 27}
The codomain is the explicitly declared output set B={-26, 0, 27}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A={2, 3, 4, 5}, B={-28, 0, 29}, ordered pairs=[(2, 29), (3, -28), (4, 0), (5, 29)] and a total function f:A→B, list the codomain in increasing order.
{-28, 0, 29}
The codomain is the explicitly declared output set B={-28, 0, 29}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A={3, 4}, B={-30, 0, 31}, ordered pairs=[(3, -30), (4, 0)] and a total function f:A→B, list the codomain in increasing order.
{-30, 0, 31}
The codomain is the explicitly declared output set B={-30, 0, 31}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A={4, 5, 6}, B={-32, 0, 33}, ordered pairs=[(4, 0), (5, 33), (6, -32)] and a total function f:A→B, list the codomain in increasing order.
{-32, 0, 33}
The codomain is the explicitly declared output set B={-32, 0, 33}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A={5, 6, 7, 8}, B={-34, 0, 35}, ordered pairs=[(5, 35), (6, -34), (7, 0), (8, 35)] and a total function f:A→B, list the codomain in increasing order.
{-34, 0, 35}
The codomain is the explicitly declared output set B={-34, 0, 35}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A={6, 7}, B={-36, 0, 37}, ordered pairs=[(6, -36), (7, 0)] and a total function f:A→B, list the codomain in increasing order.
{-36, 0, 37}
The codomain is the explicitly declared output set B={-36, 0, 37}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A={7, 8, 9}, B={-38, 0, 39}, ordered pairs=[(7, 0), (8, 39), (9, -38)] and a total function f:A→B, list the codomain in increasing order.
{-38, 0, 39}
The codomain is the explicitly declared output set B={-38, 0, 39}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A={8, 9, 10, 11}, B={-40, 0, 41}, ordered pairs=[(8, 41), (9, -40), (10, 0), (11, 41)] and a total function f:A→B, list the codomain in increasing order.
{-40, 0, 41}
The codomain is the explicitly declared output set B={-40, 0, 41}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A={9, 10}, B={-42, 0, 43}, ordered pairs=[(9, -42), (10, 0)] and a total function f:A→B, list the codomain in increasing order.
{-42, 0, 43}
The codomain is the explicitly declared output set B={-42, 0, 43}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A={10, 11, 12}, B={-44, 0, 45}, ordered pairs=[(10, 0), (11, 45), (12, -44)] and a total function f:A→B, list the codomain in increasing order.
{-44, 0, 45}
The codomain is the explicitly declared output set B={-44, 0, 45}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A={11, 12, 13, 14}, B={-46, 0, 47}, ordered pairs=[(11, 47), (12, -46), (13, 0), (14, 47)] and a total function f:A→B, list the codomain in increasing order.
{-46, 0, 47}
The codomain is the explicitly declared output set B={-46, 0, 47}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A={12, 13}, B={-48, 0, 49}, ordered pairs=[(12, -48), (13, 0)] and a total function f:A→B, list the codomain in increasing order.
{-48, 0, 49}
The codomain is the explicitly declared output set B={-48, 0, 49}; it is not guessed from the table.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-codomain-set · candidate
Given the explicit declaration A=∅, B={-2, 0, 3}, ordered pairs=[] and a total function f:A→B, list the attained range in increasing order.
∅
Collect the outputs that actually occur and remove duplicates. The range is ∅; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A=∅, B=∅, ordered pairs=[] and a total function f:A→B, list the attained range in increasing order.
∅
Collect the outputs that actually occur and remove duplicates. The range is ∅; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A={-10, -9, -8, -7}, B={-4, 0, 5}, ordered pairs=[(-10, 5), (-9, -4), (-8, 0), (-7, 5)] and a total function f:A→B, list the attained range in increasing order.
{-4, 0, 5}
Collect the outputs that actually occur and remove duplicates. The range is {-4, 0, 5}; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A={-9, -8}, B={-6, 0, 7}, ordered pairs=[(-9, -6), (-8, 0)] and a total function f:A→B, list the attained range in increasing order.
{-6, 0}
Collect the outputs that actually occur and remove duplicates. The range is {-6, 0}; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A={-8, -7, -6}, B={-8, 0, 9}, ordered pairs=[(-8, 0), (-7, 9), (-6, -8)] and a total function f:A→B, list the attained range in increasing order.
{-8, 0, 9}
Collect the outputs that actually occur and remove duplicates. The range is {-8, 0, 9}; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A={-7, -6, -5, -4}, B={-10, 0, 11}, ordered pairs=[(-7, 11), (-6, -10), (-5, 0), (-4, 11)] and a total function f:A→B, list the attained range in increasing order.
{-10, 0, 11}
Collect the outputs that actually occur and remove duplicates. The range is {-10, 0, 11}; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A={-6, -5}, B={-12, 0, 13}, ordered pairs=[(-6, -12), (-5, 0)] and a total function f:A→B, list the attained range in increasing order.
{-12, 0}
Collect the outputs that actually occur and remove duplicates. The range is {-12, 0}; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A={-5, -4, -3}, B={-14, 0, 15}, ordered pairs=[(-5, 0), (-4, 15), (-3, -14)] and a total function f:A→B, list the attained range in increasing order.
{-14, 0, 15}
Collect the outputs that actually occur and remove duplicates. The range is {-14, 0, 15}; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A={-4, -3, -2, -1}, B={-16, 0, 17}, ordered pairs=[(-4, 17), (-3, -16), (-2, 0), (-1, 17)] and a total function f:A→B, list the attained range in increasing order.
{-16, 0, 17}
Collect the outputs that actually occur and remove duplicates. The range is {-16, 0, 17}; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A={-3, -2}, B={-18, 0, 19}, ordered pairs=[(-3, -18), (-2, 0)] and a total function f:A→B, list the attained range in increasing order.
{-18, 0}
Collect the outputs that actually occur and remove duplicates. The range is {-18, 0}; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A={-2, -1, 0}, B={-20, 0, 21}, ordered pairs=[(-2, 0), (-1, 21), (0, -20)] and a total function f:A→B, list the attained range in increasing order.
{-20, 0, 21}
Collect the outputs that actually occur and remove duplicates. The range is {-20, 0, 21}; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A={-1, 0, 1, 2}, B={-22, 0, 23}, ordered pairs=[(-1, 23), (0, -22), (1, 0), (2, 23)] and a total function f:A→B, list the attained range in increasing order.
{-22, 0, 23}
Collect the outputs that actually occur and remove duplicates. The range is {-22, 0, 23}; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A={0, 1}, B={-24, 0, 25}, ordered pairs=[(0, -24), (1, 0)] and a total function f:A→B, list the attained range in increasing order.
{-24, 0}
Collect the outputs that actually occur and remove duplicates. The range is {-24, 0}; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A={1, 2, 3}, B={-26, 0, 27}, ordered pairs=[(1, 0), (2, 27), (3, -26)] and a total function f:A→B, list the attained range in increasing order.
{-26, 0, 27}
Collect the outputs that actually occur and remove duplicates. The range is {-26, 0, 27}; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A={2, 3, 4, 5}, B={-28, 0, 29}, ordered pairs=[(2, 29), (3, -28), (4, 0), (5, 29)] and a total function f:A→B, list the attained range in increasing order.
{-28, 0, 29}
Collect the outputs that actually occur and remove duplicates. The range is {-28, 0, 29}; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A={3, 4}, B={-30, 0, 31}, ordered pairs=[(3, -30), (4, 0)] and a total function f:A→B, list the attained range in increasing order.
{-30, 0}
Collect the outputs that actually occur and remove duplicates. The range is {-30, 0}; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A={4, 5, 6}, B={-32, 0, 33}, ordered pairs=[(4, 0), (5, 33), (6, -32)] and a total function f:A→B, list the attained range in increasing order.
{-32, 0, 33}
Collect the outputs that actually occur and remove duplicates. The range is {-32, 0, 33}; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A={5, 6, 7, 8}, B={-34, 0, 35}, ordered pairs=[(5, 35), (6, -34), (7, 0), (8, 35)] and a total function f:A→B, list the attained range in increasing order.
{-34, 0, 35}
Collect the outputs that actually occur and remove duplicates. The range is {-34, 0, 35}; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A={6, 7}, B={-36, 0, 37}, ordered pairs=[(6, -36), (7, 0)] and a total function f:A→B, list the attained range in increasing order.
{-36, 0}
Collect the outputs that actually occur and remove duplicates. The range is {-36, 0}; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A={7, 8, 9}, B={-38, 0, 39}, ordered pairs=[(7, 0), (8, 39), (9, -38)] and a total function f:A→B, list the attained range in increasing order.
{-38, 0, 39}
Collect the outputs that actually occur and remove duplicates. The range is {-38, 0, 39}; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A={8, 9, 10, 11}, B={-40, 0, 41}, ordered pairs=[(8, 41), (9, -40), (10, 0), (11, 41)] and a total function f:A→B, list the attained range in increasing order.
{-40, 0, 41}
Collect the outputs that actually occur and remove duplicates. The range is {-40, 0, 41}; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A={9, 10}, B={-42, 0, 43}, ordered pairs=[(9, -42), (10, 0)] and a total function f:A→B, list the attained range in increasing order.
{-42, 0}
Collect the outputs that actually occur and remove duplicates. The range is {-42, 0}; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A={10, 11, 12}, B={-44, 0, 45}, ordered pairs=[(10, 0), (11, 45), (12, -44)] and a total function f:A→B, list the attained range in increasing order.
{-44, 0, 45}
Collect the outputs that actually occur and remove duplicates. The range is {-44, 0, 45}; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A={11, 12, 13, 14}, B={-46, 0, 47}, ordered pairs=[(11, 47), (12, -46), (13, 0), (14, 47)] and a total function f:A→B, list the attained range in increasing order.
{-46, 0, 47}
Collect the outputs that actually occur and remove duplicates. The range is {-46, 0, 47}; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
Given the explicit declaration A={12, 13}, B={-48, 0, 49}, ordered pairs=[(12, -48), (13, 0)] and a total function f:A→B, list the attained range in increasing order.
{-48, 0}
Collect the outputs that actually occur and remove duplicates. The range is {-48, 0}; unattained codomain elements are not added.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-range-set · candidate
For the explicit data A=∅, B=∅, ordered pairs=[], does the table define a complete total function f:A→B? Answer Yes or No.
Yes
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is Yes; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={0}, B=∅, ordered pairs=[], does the table define a complete total function f:A→B? Answer Yes or No.
No
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is No; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={0}, B=∅, ordered pairs=[(0, 0)], does the table define a complete total function f:A→B? Answer Yes or No.
No
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is No; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={-9, -8}, B={-6, 0, 7}, ordered pairs=[(-9, -6), (-8, 0), (-9, 0)], does the table define a complete total function f:A→B? Answer Yes or No.
No
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is No; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={-8, -7, -6}, B={-8, 0, 9}, ordered pairs=[(-8, 0), (-7, 9), (-6, -8), (-5, -8)], does the table define a complete total function f:A→B? Answer Yes or No.
No
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is No; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={-7, -6, -5, -4}, B={-10, 0, 11}, ordered pairs=[(-7, 11), (-6, -10), (-5, 0), (-4, 11)], does the table define a complete total function f:A→B? Answer Yes or No.
Yes
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is Yes; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={-6, -5}, B={-12, 0, 13}, ordered pairs=[(-5, 0)], does the table define a complete total function f:A→B? Answer Yes or No.
No
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is No; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={-5, -4, -3}, B={-14, 0, 15}, ordered pairs=[(-5, 107), (-4, 15), (-3, -14)], does the table define a complete total function f:A→B? Answer Yes or No.
No
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is No; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={-4, -3, -2, -1}, B={-16, 0, 17}, ordered pairs=[(-4, 17), (-3, -16), (-2, 0), (-1, 17), (-4, -16)], does the table define a complete total function f:A→B? Answer Yes or No.
No
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is No; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={-3, -2}, B={-18, 0, 19}, ordered pairs=[(-3, -18), (-2, 0), (-1, -18)], does the table define a complete total function f:A→B? Answer Yes or No.
No
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is No; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={-2, -1, 0}, B={-20, 0, 21}, ordered pairs=[(-2, 0), (-1, 21), (0, -20)], does the table define a complete total function f:A→B? Answer Yes or No.
Yes
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is Yes; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={-1, 0, 1, 2}, B={-22, 0, 23}, ordered pairs=[(0, -22), (1, 0), (2, 23)], does the table define a complete total function f:A→B? Answer Yes or No.
No
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is No; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={0, 1}, B={-24, 0, 25}, ordered pairs=[(0, 112), (1, 0)], does the table define a complete total function f:A→B? Answer Yes or No.
No
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is No; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={1, 2, 3}, B={-26, 0, 27}, ordered pairs=[(1, 0), (2, 27), (3, -26), (1, 27)], does the table define a complete total function f:A→B? Answer Yes or No.
No
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is No; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={2, 3, 4, 5}, B={-28, 0, 29}, ordered pairs=[(2, 29), (3, -28), (4, 0), (5, 29), (6, -28)], does the table define a complete total function f:A→B? Answer Yes or No.
No
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is No; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={3, 4}, B={-30, 0, 31}, ordered pairs=[(3, -30), (4, 0)], does the table define a complete total function f:A→B? Answer Yes or No.
Yes
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is Yes; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={4, 5, 6}, B={-32, 0, 33}, ordered pairs=[(5, 33), (6, -32)], does the table define a complete total function f:A→B? Answer Yes or No.
No
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is No; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={5, 6, 7, 8}, B={-34, 0, 35}, ordered pairs=[(5, 117), (6, -34), (7, 0), (8, 35)], does the table define a complete total function f:A→B? Answer Yes or No.
No
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is No; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={6, 7}, B={-36, 0, 37}, ordered pairs=[(6, -36), (7, 0), (6, 0)], does the table define a complete total function f:A→B? Answer Yes or No.
No
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is No; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={7, 8, 9}, B={-38, 0, 39}, ordered pairs=[(7, 0), (8, 39), (9, -38), (10, -38)], does the table define a complete total function f:A→B? Answer Yes or No.
No
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is No; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={8, 9, 10, 11}, B={-40, 0, 41}, ordered pairs=[(8, 41), (9, -40), (10, 0), (11, 41)], does the table define a complete total function f:A→B? Answer Yes or No.
Yes
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is Yes; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={9, 10}, B={-42, 0, 43}, ordered pairs=[(10, 0)], does the table define a complete total function f:A→B? Answer Yes or No.
No
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is No; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={10, 11, 12}, B={-44, 0, 45}, ordered pairs=[(10, 122), (11, 45), (12, -44)], does the table define a complete total function f:A→B? Answer Yes or No.
No
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is No; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={11, 12, 13, 14}, B={-46, 0, 47}, ordered pairs=[(11, 47), (12, -46), (13, 0), (14, 47), (11, -46)], does the table define a complete total function f:A→B? Answer Yes or No.
No
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is No; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
For the explicit data A={12, 13}, B={-48, 0, 49}, ordered pairs=[(12, -48), (13, 0), (14, -48)], does the table define a complete total function f:A→B? Answer Yes or No.
No
Check that every input in A has exactly one output in B and that no row uses an extra input. The result is No; the same rule covers an empty domain.
Reviewed step-by-step derivation
Domain, codomain, and range · qf-function-table-validity · candidate
Canonical question JSONL · English JSONL · Validation report