select the correct answer.

what is the zero of the function represented by this graph?

$x = -6$
$x = 5$
$x = -5$
$x = 6$

Question

select the correct answer.

what is the zero of the function represented by this graph?

$x = -6$
$x = 5$
$x = -5$
$x = 6$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Radical Function Graphs", "Graph Intercepts" ], "new_concepts": [], "current_concepts": [ "Radical Function Graphs", "Graph Intercepts", "Zeros of Polynomial Functions" ] } ## Identify the function type and key points from the graph $$ \begin{aligned} &\text{Starting point of the radical function: } (-6, 0)\ &\text{Other clear integer points on the curve: } (-5, 1), (-2, 2), (3, 3) \end{aligned} $$ ## Determine the equation of the function $$ \begin{aligned} &y = a\sqrt{x - h} + k\ &(h, k) = (-6, 0) \implies y = a\sqrt{x + 6}\ &\text{Substitute } (-5, 1): 1 = a\sqrt{-5 + 6} \implies a = 1\ &y = \sqrt{x + 6} \end{aligned} $$ ## Find the zero of the function $$ \begin{aligned} &y = 0 \implies \sqrt{x + 6} = 0\ &x + 6 = 0 \implies x = -6 \end{aligned} $$

(A) $x = -6$

(B) $x = 5$

(C) $x = -5$

(D) $x = 6$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Graph Intercepts" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the function type and key points from the graph

Determine the equation of the function

Find the zero of the function

Answer: