write an equation for the function graphed above

$y =$

enter abs(x) for $|x|$

Question

write an equation for the function graphed above

$y =$

enter abs(x) for $|x|$

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": [ "Function Transformations" ], "new_concepts": [ "Absolute Value Transformations" ], "current_concepts": [ "Function Transformations", "Absolute Value Transformations" ] } ## Identify the vertex of the absolute value function Using the *Function Transformations* knowledge point $$ (h, k) = (2, -2) $$ ## Determine the vertical stretch or compression factor Using the *Function Transformations* knowledge point $$ \begin{aligned} y &= a|x - h| + k \ -4 &= a|0 - 2| - 2 \ -4 &= 2a - 2 \ 2a &= -2 \ a &= -1 \end{aligned} $$ ## Write the final equation Using the *Function Transformations* knowledge point $$ y = -|x - 2| - 2 $$ Write an equation for the function graphed above $y =$ $-\text{abs}(x-2)-2$ { "elements": [ { "type": "point", "params": [[2, -2]], "properties": { "name": "Vertex (2, -2)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[0, -4]], "properties": { "name": "(0, -4)", "size": 4, "color": "#5583F2", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "-Math.abs(x-2)-2", "latex": "-|x-2|-2"}, -6, 6], "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 function

Determine the vertical stretch or compression factor

Write the final equation

Answer: