determine the maximum possible number of turning points for the graph of the function.
(f(x) = (x + 2)(x + 7)(5x - 5))

a. 2
b. 0
c. 5
d. 3

Question

determine the maximum possible number of turning points for the graph of the function.
(f(x) = (x + 2)(x + 7)(5x - 5))

a. 2
b. 0
c. 5
d. 3

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Degree of Polynomial", "Turning Points" ], "new_concepts": [], "current_concepts": [ "Polynomial Functions", "Degree of Polynomial", "Turning Points" ] } ## Determine the degree of the polynomial Using the *Degree of Polynomial* knowledge point $$ \begin{aligned} f(x) &= (x + 2)(x + 7)(5x - 5) \ \text{Degree } (n) &= 1 + 1 + 1 = 3 \end{aligned} $$ ## Find the maximum number of turning points Using the *Turning Points* knowledge point $$ \begin{aligned} \text{Max Turning Points} &= n - 1 \ &= 3 - 1 \ &= 2 \end{aligned} $$

(A) 2

(B) 0

(C) 5

(D) 3

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Turning Points" ] }

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QUESTION IMAGE

Question

Explanation:

Determine the degree of the polynomial

Find the maximum number of turning points

Answer: