Question

Algebra 2 pls help lol

Answer 1

Answer:

• right -2
• down 2
• reflected in the y-axis
• compressed by a factor of 1/2

Step-by-step explanation:

The order of the transformations affects the values used for translation. Here, the translation is described before the reflection and compression.

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reflection

The grayed-out graph of the square root function opens to the right. The darker graph of the transformed function opens to the left, so the reflection is across the y-axis.

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compression

The square root function goes through the point (1, 1), that is, 1 unit right of the vertex, and 1 unit up. The transformed function goes through the point (1, -1/2), that is, 1 unit left of the vertex and 1/2 unit up. The vertical height of 1 unit on the original graph is compressed to a height of 1/2 unit on the transformed graph. Vertical compression is by a factor of 1/2.

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translation

The description of the transformation gives the translation before the reflection and compression. So, to find where the uncompressed and unreflected vertex is, we need to reverse those transformations.

Expanding the transformed square root graph by a factor of 2 will undo its compression by a factor of 1/2. That will move the vertex from (2, -1) to (2, 2×(-1)) = (2, -2).

Reflecting this expanded function back across the y-axis will undo the original reflection. That moves the vertex from (2, -2) to (-2, -2). This is where the original translation left the function's vertex before the reflection and compression moved it to the location shown.

The translation is right -2 and down 2.

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Additional comment

It is possible that you will get pushback on these answers. If so, you should have your teacher demonstrate the transformations in the order described.

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In the order described, we have ...

  $f(x)=\sqrt{x}\\\\f_1(x)=\sqrt{x-(-2)}=\sqrt{x+2}\qquad\text{translation right -2}\\\\f_2(x)=\sqrt{x+2}-2\qquad\text{translation down 2}\\\\f_3(x)=\sqrt{-x+2}-2\qquad\text{reflection in the y-axis}\\\\g(x)=\dfrac{1}{2}(\sqrt{-x+2}-2)\qquad\text{compression vertically by \dfrac{1}{2} }$

The attached graph shows the result of this sequence of transformations.

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If the reflection and compression were done before the translation, then the translation would be 2 right and 1 down.