the graph shows $g(x)$, which is a translation of $f(x) = |x|$. write the function rule for $g(x)$.

write your answer in the form $a|x - h| + k$, where $a$, $h$, and $k$ are integers or simplified fractions.

$g(x) = $

Question

the graph shows $g(x)$, which is a translation of $f(x) = |x|$. write the function rule for $g(x)$.

write your answer in the form $a|x - h| + k$, where $a$, $h$, and $k$ are integers or simplified fractions.

$g(x) = $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Absolute Value Transformations", "Vertex of Absolute Value" ], "new_concepts": [], "current_concepts": [ "Absolute Value Transformations", "Vertex of Absolute Value" ] } ## Identify the vertex of the graph Using the *Vertex of Absolute Value* knowledge point $$ (h, k) = (-6, 0) $$ ## Determine the horizontal and vertical shifts Using the *Absolute Value Transformations* knowledge point $$ \begin{aligned} h &= -6\ k &= 0 \end{aligned} $$ ## Determine the vertical stretch factor Using the *Absolute Value Transformations* knowledge point $$ \begin{aligned} g(0) &= 6\ a|0 - (-6)| + 0 &= 6\ 6a &= 6\ a &= 1 \end{aligned} $$ ## Write the final function rule Using the *Absolute Value Transformations* knowledge point $$ g(x) = |x + 6| $$ The graph shows $g(x)$, which is a translation of $f(x) = |x|$. Write the function rule for $g(x)$. Write your answer in the form $a|x - h| + k$, where $a$, $h$, and $k$ are integers or simplified fractions. $g(x) =$ $|x + 6|$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Absolute Value Transformations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the vertex of the graph

Determine the horizontal and vertical shifts

Determine the vertical stretch factor

Write the final function rule

Answer: