consider the graph of $f$ below.

a) is the degree of $f$ even or odd?
- odd
- even

b) what is the sign of the leading coefficient of $f$?
- positive
- negative

Question

consider the graph of $f$ below.

a) is the degree of $f$ even or odd?
- odd
- even

b) what is the sign of the leading coefficient of $f$?
- positive
- negative

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Degree", "Leading Coefficient" ], "new_concepts": [], "current_concepts": [ "Polynomial Degree", "Leading Coefficient", "End Behavior" ] } ## Analyze end behavior for degree parity $$ \begin{aligned} &\lim_{x \to -\infty} f(x) = -\infty\ &\lim_{x \to \infty} f(x) = -\infty\ &\text{Both ends point in the same direction } \implies \text{even degree} \end{aligned} $$ ## Determine sign of leading coefficient $$ \begin{aligned} &\lim_{x \to \pm\infty} f(x) = -\infty\ &\text{Ends point downwards } \implies \text{negative leading coefficient} \end{aligned} $$ ## Question a odd even ## Question b positive

negative

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Degree" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze end behavior for degree parity

Determine sign of leading coefficient

Answer:

Question a

Question b