complete the statements about the key features of the graph of (f(x) = x^5 - 9x^3).

as (x) goes to negative infinity, (f(x)) goes to infinity, and as (x) goes to positive infinity, (f(x)) goes to infinity.

Question

complete the statements about the key features of the graph of (f(x) = x^5 - 9x^3).

as (x) goes to negative infinity, (f(x)) goes to   infinity, and as (x) goes to positive infinity, (f(x)) goes to   infinity.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "End Behavior", "Polynomial Degree", "Leading Coefficient" ], "current_concepts": [ "End Behavior", "Polynomial Degree", "Leading Coefficient" ] } ## Determine the leading term of the polynomial $$ \begin{aligned} &f(x) = x^5 - 9x^3\ &\text{Leading term: } x^5\ &\text{Degree: } 5 \quad (\text{odd})\ &\text{Leading coefficient: } 1 \quad (\text{positive}) \end{aligned} $$ ## Analyze end behavior as x approaches negative infinity $$ \begin{aligned} &\lim_{x \to -\infty} f(x) = \lim_{x \to -\infty} x^5 = -\infty \end{aligned} $$ ## Analyze end behavior as x approaches positive infinity $$ \begin{aligned} &\lim_{x \to \infty} f(x) = \lim_{x \to \infty} x^5 = \infty \end{aligned} $$ Complete the statements about the key features of the graph of $f(x) = x^5 - 9x^3$. As $x$ goes to negative infinity, $f(x)$ goes to negative infinity, and as $x$ goes to positive infinity, $f(x)$ goes to positive infinity. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "End Behavior" ] }

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Question

Explanation:

Determine the leading term of the polynomial

Analyze end behavior as x approaches negative infinity

Analyze end behavior as x approaches positive infinity

Answer: