identify the graph of $y = x^3$

the domain of $y = x^3$ is
all real numbers.
$x 0$
$x \ge 0$

Question

identify the graph of $y = x^3$

the domain of $y = x^3$ is
all real numbers.
$x > 0$
$x \ge 0$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Cubic Function Analysis", "Domain of Rational Functions" ], "new_concepts": [ "Domain of Polynomial Functions" ], "current_concepts": [ "Cubic Function Analysis", "Domain of Polynomial Functions" ] } ## Identify the graph of $y = x^3$ Using the *Cubic Function Analysis* knowledge point $$ \begin{aligned} &x = -2 \implies y = (-2)^3 = -8\ &x = -1 \implies y = (-1)^3 = -1\ &x = 0 \implies y = 0^3 = 0\ &x = 1 \implies y = 1^3 = 1\ &x = 2 \implies y = 2^3 = 8 \end{aligned} $$ The second graph passes through $(0,0)$, $(1,1)$, and $(-1,-1)$. ## Determine the domain of $y = x^3$ Using the *Domain of Rational Functions* knowledge point $$ \begin{aligned} &\text{The function } y = x^3 \text{ is a polynomial function.}\ &\text{Polynomials are defined for all real numbers.}\ &\text{Domain: } (-\infty, \infty) \end{aligned} $$ ## Question 1 (A) Exponential-like curve passing through (0,1) (B) S-shaped cubic curve passing through (0,0) ## Question 2 all real numbers.

$x > 0$

$x \ge 0$

{ "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Cubic Function Analysis" ] }

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Explanation:

Identify the graph of \(y = x^3\)

Determine the domain of \(y = x^3\)

Answer:

Question 1

Question 2