select all the correct answers.

which equations represent functions?

$2x + 3y = 10$
$4x = 16$
$2x - 3 = 14$
$3y = 18$
$14.6 = 2x$

Question

select all the correct answers.

which equations represent functions?

$2x + 3y = 10$
$4x = 16$
$2x - 3 = 14$
$3y = 18$
$14.6 = 2x$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Functions" ], "new_concepts": [ "Definition of a Function", "Equations in Two Variables" ], "current_concepts": [ "Linear Functions", "Definition of a Function", "Equations in Two Variables" ] } ## Analyze the definition of a function $$ y = f(x) $$ A relation represents a function if each input $x$ maps to exactly one output $y$. For equations in two variables $x$ and $y$, we check if we can express $y$ uniquely in terms of $x$. ## Evaluate each given equation $$ \begin{aligned} &1.\quad 2x + 3y = 10 \implies y = \frac{10 - 2x}{3} \quad (\text{Unique } y \text{ for each } x) \ &2.\quad 4x = 16 \implies x = 4 \quad (\text{No } y \text{ variable, vertical line, not a function of } x) \ &3.\quad 2x - 3 = 14 \implies x = 8.5 \quad (\text{No } y \text{ variable, vertical line, not a function of } x) \ &4.\quad 3y = 18 \implies y = 6 \quad (\text{Constant function, unique } y \text{ for each } x) \ &5.\quad 14.6 = 2x \implies x = 7.3 \quad (\text{No } y \text{ variable, vertical line, not a function of } x) \end{aligned} $$ ## Identify the correct options $$ \text{Functions: } 2x + 3y = 10 \quad \text{and} \quad 3y = 18 $$

(A) $2x + 3y = 10$

(B) $4x = 16$

(C) $2x - 3 = 14$

(D) $3y = 18$

(E) $14.6 = 2x$

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

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QUESTION IMAGE

Question

Explanation:

Analyze the definition of a function

Evaluate each given equation

Identify the correct options

Answer: