select the correct answer.

which relation does not represent a function?

$\{(3, 0), (0, 3)\}$
$\{(6, -2), (5, -2)\}$
$\{(3, 4), (3, 5)\}$
$\{(5, 5), (-5, -5)\}$
$\{(1, -2), (-2, 1)\}$

Question

select the correct answer.

which relation does not represent a function?

$\{(3, 0), (0, 3)\}$
$\{(6, -2), (5, -2)\}$
$\{(3, 4), (3, 5)\}$
$\{(5, 5), (-5, -5)\}$
$\{(1, -2), (-2, 1)\}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Function Definition", "Relations and Functions" ], "current_concepts": [ "Function Definition", "Relations and Functions" ] } ## Define the condition for a relation to be a function $$ \forall (x_1, y_1), (x_2, y_2) \in R, \quad x_1 = x_2 \implies y_1 = y_2 $$ ## Evaluate each relation for duplicate inputs with different outputs $$ \begin{aligned} &\{(3, 0), (0, 3)\}: \quad 3 \to 0, \quad 0 \to 3 \quad (\text{Function}) \ &\{(6, -2), (5, -2)\}: \quad 6 \to -2, \quad 5 \to -2 \quad (\text{Function}) \ &\{(3, 4), (3, 5)\}: \quad 3 \to 4, \quad 3 \to 5 \quad (4 eq 5 \implies \text{Not a Function}) \ &\{(5, 5), (-5, -5)\}: \quad 5 \to 5, \quad -5 \to -5 \quad (\text{Function}) \ &\{(1, -2), (-2, 1)\}: \quad 1 \to -2, \quad -2 \to 1 \quad (\text{Function}) \end{aligned} $$ ## Identify the non-function relation $$ R = \{(3, 4), (3, 5)\} $$

A. $\{(3, 0), (0, 3)\}$

B. $\{(6, -2), (5, -2)\}$

C. $\{(3, 4), (3, 5)\}$

D. $\{(5, 5), (-5, -5)\}$

E. $\{(1, -2), (-2, 1)\}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Function Definition" ] }

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QUESTION IMAGE

Question

Explanation:

Define the condition for a relation to be a function

Evaluate each relation for duplicate inputs with different outputs

Identify the non-function relation

Answer: