To accurately determine how the parent function \( f(x) = |x| \) was transformed to produce the graphed function, we need to analyze the appearance of the graph described in your question.
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Upward Facing V-Shape: The parent function \( f(x) = |x| \) is already an upward facing V-shape.
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Range of the x-axis (-3 to 3) and y-axis (0 to 3): This indicates that the height of the graph does not exceed 3 on the y-axis.
Considering these aspects, the transformations applied to the parent function \( f(x) = |x| \) would involve vertical or horizontal translations, stretches, or compressions. Here’s what each option implies:
- Vertically translated down: This would lower the entire graph, not applicable if the lowest point is still at (0,0).
- Horizontally compressed: This would make the V-shape narrower, also not applicable as no such effect is mentioned.
- Vertically translated up: This would lift the entire graph, again not applicable if the vertex remains at (0,0).
- Horizontally stretched: This would widen the V-shape, which could lead to a different appearance.
Given the description, the graph most likely remains as the parent function, with no indication of vertical or horizontal transformations. However, based on common classroom examples and standard transformations, the most plausible choice based on the provided options would be that the graph could have been vertically translated up, as the entire shape retains the common appearance of the V-shape but indicates that there could still be a uniform transformation happening.
Therefore, I would cautiously interpret the transformation as:
The parent function was vertically translated up.