$-\infty

Question

$-\infty < x < 1$
$-\infty < x < \infty$
$-\infty < x < 2$
$1 < x < \infty$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Increasing Intervals", "Quadratic Functions", "Vertex of Parabola" ], "new_concepts": [], "current_concepts": [ "Increasing Intervals", "Quadratic Functions", "Vertex of Parabola" ] } ## Identify the vertex of the parabola The given graph is a downward-opening parabola. The peak or vertex of this parabola is located at the point $(1, 1)$. ## Determine the interval where the function is increasing A function is increasing where its graph rises from left to right. For this downward-opening parabola, the graph rises for all $x$-values to the left of the vertex's $x$-coordinate. $$ x < 1 \implies -\infty < x < 1 $$ ## Match with the given options The interval of increase is $-\infty < x < 1$, which corresponds to the first option.

(A) $-\infty < x < 1$

(B) $-\infty < x < \infty$

(C) $-\infty < x < 2$

(D) $1 < x < \infty$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Increasing Intervals" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the vertex of the parabola

Determine the interval where the function is increasing

Match with the given options

Answer: