the graph to the right is a complete graph, that is, it is continuous and displays the functions end behavior. all zeros are integers. answer the following questions.

-6, 6, 1 by -100, 10, 10

(a) list the zeros whose multiplicity is even. select the correct choice below and fill in any answer boxes within your choice.

a.
(type an integers or a simplified fractions. use a comma to separate answers as needed.)

b. there are no such zeros.

Question

the graph to the right is a complete graph, that is, it is continuous and displays the functions end behavior. all zeros are integers. answer the following questions.

-6, 6, 1 by -100, 10, 10

(a) list the zeros whose multiplicity is even. select the correct choice below and fill in any answer boxes within your choice.

a.
(type an integers or a simplified fractions. use a comma to separate answers as needed.)

b. there are no such zeros.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Multiplicity of Zeros", "Polynomial Graphs" ], "current_concepts": [ "Multiplicity of Zeros", "Polynomial Graphs", "Zeros of Polynomials" ] } ## Identify x-intercepts and behavior $$ \begin{aligned} &\text{x-axis range: } [-6, 6] \text{ with tick spacing of } 1\ &\text{x-intercepts (zeros): } x = -4, \quad x = 2\ &\text{Behavior at } x = -4: \text{ tangent to the x-axis (touches and turns around)}\ &\text{Behavior at } x = 2: \text{ tangent to the x-axis (touches and turns around)} \end{aligned} $$ ## Determine multiplicity type $$ \begin{aligned} &\text{Tangent behavior (touch and turn) } \implies \text{even multiplicity}\ &\text{Crossing behavior } \implies \text{odd multiplicity}\ &\text{Zeros with even multiplicity: } -4, 2 \end{aligned} $$

A. -4, 2

B. There are no such zeros.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Multiplicity of Zeros" ] }

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Question

Explanation:

Identify x-intercepts and behavior

Determine multiplicity type

Answer: