list the interval(s) on which f is increasing.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Intervals of Increase and Decrease" ], "new_concepts": [], "current_concepts": [ "Intervals of Increase and Decrease", "Graph Analysis" ] } ## Identify local extrema and key coordinates $$ \begin{aligned} &\text{Left endpoint: } (-12, -1) \ &\text{Local minimum 1: } (-10, -5) \ &\text{Local maximum 1: } (-4, 5) \ &\text{Local minimum 2: } (-2, -1) \ &\text{Local maximum 2: } (0, 9) \ &\text{Local minimum 3: } (3, -1) \ &\text{Right endpoint: } (5, 2) \end{aligned} $$ ## Determine intervals where the function rises from left to right $$ \begin{aligned} &\text{Increasing from } x = -10 \text{ to } x = -4 \ &\text{Increasing from } x = -2 \text{ to } x = 0 \ &\text{Increasing from } x = 3 \text{ to } x = 5 \end{aligned} $$ ## Express the increasing intervals in interval notation $$ [-10, -4] \cup [-2, 0] \cup [3, 5] $$ The intervals on which $f$ is increasing are $[-10, -4] \cup [-2, 0] \cup [3, 5]$ (or written with open intervals as $(-10, -4) \cup (-2, 0) \cup (3, 5)$). { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Intervals of Increase and Decrease" ] }

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Identify local extrema and key coordinates

Determine intervals where the function rises from left to right

Express the increasing intervals in interval notation

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