using the graph of the function (y = f(x)), answer the following questions.

a) on what intervals is (f) increasing? enter your answer in interval notation.

b) on what intervals is (f) decreasing? enter your answer in interval notation.

Question

using the graph of the function (y = f(x)), answer the following questions.

a) on what intervals is (f) increasing? enter your answer in interval notation.

b) on what intervals is (f) decreasing? enter your answer in interval notation.

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Interval Notation" ], "new_concepts": [ "Increasing Intervals", "Decreasing Intervals" ], "current_concepts": [ "Interval Notation", "Increasing Intervals", "Decreasing Intervals" ] } ## Identify local extrema from the graph $$ \begin{aligned} &\text{Local maximum at } x = -1\ &\text{Local minimum at } x = 1 \end{aligned} $$ ## Determine intervals of increase $$ \begin{aligned} &\text{Increasing where the graph rises from left to right:}\ &(-\infty, -1) \cup (1, \infty) \end{aligned} $$ ## Determine intervals of decrease $$ \begin{aligned} &\text{Decreasing where the graph falls from left to right:}\ &(-1, 1) \end{aligned} $$ ## Question a $(-\infty, -1) \cup (1, \infty)$ ## Question b $(-1, 1)$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Increasing and Decreasing Intervals" ] }

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QUESTION IMAGE

Question

Explanation:

Identify local extrema from the graph

Determine intervals of increase

Determine intervals of decrease

Answer:

Question a

Question b