given the function $f(x) = 3x^2 + 6x + 9$, if $x = -1$, what is $f(x)$? what point is on the graph of $f$?

a. $6; (-1,6)$
b. $6; (6,-1)$
c. $18; (18,-1)$
d. $18; (-1,18)$

Question

given the function $f(x) = 3x^2 + 6x + 9$, if $x = -1$, what is $f(x)$? what point is on the graph of $f$?

a. $6; (-1,6)$
b. $6; (6,-1)$
c. $18; (18,-1)$
d. $18; (-1,18)$

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": [ "Function Evaluation", "Polynomial Evaluation" ], "new_concepts": [], "current_concepts": [ "Function Evaluation", "Polynomial Evaluation", "Graph Analysis" ] } ## Evaluate the function at the given input Using the *Function Evaluation* and *Polynomial Evaluation* knowledge points $$ \begin{aligned} f(-1) &= 3(-1)^2 + 6(-1) + 9 \ &= 3(1) - 6 + 9 \ &= 3 - 6 + 9 \ &= 6 \end{aligned} $$ ## Determine the corresponding point on the graph Using the *Function Evaluation* knowledge point $$ \begin{aligned} &\text{Input } x = -1 \implies \text{Output } y = f(-1) = 6 \ &\text{Point: } (x, y) = (-1, 6) \end{aligned} $$

A. 6; $(-1,6)$

B. 6; $(6,-1)$

C. 18; $(18,-1)$

D. 18; $(-1,18)$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Function Evaluation" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Evaluate the function at the given input

Determine the corresponding point on the graph

Answer: