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": true, "concepts_used": [ "Absolute Value Transformations", "Vertex of Absolute Value" ], "new_concepts": [], "current_concepts": [ "Absolute Value Transformations", "Vertex of Absolute Value", "Function Rules" ] } ## Identify the vertex of the absolute value graph Using the *Vertex of Absolute Value* knowledge point $$ (h, k) = (-7, -7) $$ ## Determine the vertical stretch or compression factor Using the *Absolute Value Transformations* knowledge point $$ \begin{aligned} &g(x) = a|x - h| + k\ &g(x) = a|x + 7| - 7\ &\text{Substitute point } (1, 1):\ &1 = a|1 + 7| - 7\ &8 = 8a\ &a = 1 \end{aligned} $$ ## Write the final function rule Using the *Absolute Value Transformations* knowledge point $$ g(x) = |x + 7| - 7 $$ 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. $g(x) =$ $|x + 7| - 7$ { "elements": [ { "type": "point", "params": [[-7, -7]], "properties": { "name": "Vertex (-7, -7)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[1, 1]], "properties": { "name": "(1, 1)", "size": 4, "color": "#F2557F", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "Math.abs(x + 7) - 7", "latex": "|x + 7| - 7"}, -10, 10], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3 } } ] } { "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 absolute value graph

Determine the vertical stretch or compression factor

Write the final function rule

Answer: