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{ "quality": "incomplete", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Piecewise Functions", "Graph Intercepts", "Function Comparison" ], "new_concepts": [], "current_concepts": [ "Piecewise Functions", "Graph Intercepts", "Function Comparison" ] } ## Determine the y-intercept of function f $$ \begin{aligned} &\text{From the graph of } f(x), \text{ the curve crosses the } y\text{-axis at } (0, 2).\ &\text{Therefore, the } y\text{-intercept of } f \text{ is } 2. \end{aligned} $$ ## Determine the y-intercept of function g $$ \begin{aligned} &\text{To find the } y\text{-intercept of } g(x), \text{ evaluate } g(0).\ &\text{Since } 0 \le 1, \text{ use the first piece: } g(x) = x - 4.\ &g(0) = 0 - 4 = -4.\ &\text{Therefore, the } y\text{-intercept of } g \text{ is } -4. \end{aligned} $$ ## Compare the y-intercepts $$ \begin{aligned} &2 > -4\ &\text{The } y\text{-intercept of } f \text{ is greater than the } y\text{-intercept of } g. \end{aligned} $$

The y-intercept of $f$ is greater than the y-intercept of $g$.

The y-intercept of $g$ is greater than the y-intercept of $f$.

The y-intercept of $f$ is equal to the y-intercept of $g$.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Piecewise Functions" ] }

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Determine the y-intercept of function f

Determine the y-intercept of function g

Compare the y-intercepts

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