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Which of the following statements correctly describes how the parent function f(x)=|x|

was dilated to result in the graphed function?

(1 point)
Responses

The parent function was horizontally compressed.
The parent function was horizontally compressed.

The parent function was vertically translated up.
The parent function was vertically translated up.

The parent function was horizontally stretched.
The parent function was horizontally stretched.

The parent function was vertically translated down.

3 answers

To determine how the parent function \( f(x) = |x| \) was transformed, we would need to know the specifics of the graphed function to analyze its changes. However, based on the types of transformations mentioned, here are some general guidelines for each statement:

  1. Horizontally compressed: This means that the graph of the function would appear to "squeeze in" towards the y-axis. For example, if the transformed function were \( f(x) = |2x| \), that would be a horizontal compression.

  2. Vertically translated up: This would mean that the entire graph moves up along the y-axis. For instance, if the function were \( f(x) = |x| + 3 \), this indicates a vertical translation up by 3 units.

  3. Horizontally stretched: This would indicate that the graph is being "pulled" away from the y-axis. If the function were \( f(x) = |0.5x| \), that indicates a horizontal stretch.

  4. Vertically translated down: This occurs when the graph moves down along the y-axis. If the function were \( f(x) = |x| - 2 \), this would be a vertical translation down by 2 units.

To provide an accurate answer, one would need to compare the parent function \( f(x) = |x| \) to the specific graphed function.

If you have the specific transformed function or graph description, please share that for a more accurate assessment!

the points are (-2,1) , (2,1)

Given the points \((-2, 1)\) and \((2, 1)\), we can analyze how the parent function \(f(x) = |x|\) has been transformed.

  1. The parent function \(f(x) = |x|\) has the key points \((-1, 1)\), \((0, 0)\), and \((1, 1)\).
  2. In this case, the key feature of the transformed points you provided is that both points have the same y-coordinate of \(1\) (for \(x = -2\) and \(x = 2\)).

This suggests that the graph has been vertically translated up. Specifically, we can deduce that the transformation that resulted in these points is a vertical translation upwards by \(1\).

Thus, the correct statement describing how the parent function \(f(x) = |x|\) was transformed to result in the graph of the new function is:

  • The parent function was vertically translated up.

If the transformed function represented is \(f(x) = |x| + 1\), this aligns with the new points where the function equals \(1\) at \(x = -2\) and \(x = 2\).