Question

A parent function and transformed function are shown: y = RootIndex 3 StartRoot x EndRoot. y = negative (0.4) RootIndex 3 StartRoot x minus 2 EndRoot Which of the following describes the graph of the transformed function compared with the parent function? Select all that apply. reflected over the x-axis translated 2 units left translated 2 units right compressed by a factor of 0.4 stretched by a factor of 0.4 translated 2 units up translated 2 units down

Answer 1

Answer: The transformed function is y = -0.4√(x - 2).

Explanation:

From the given equation, we can identify the following transformations:

Reflected over the x-axis: The negative sign in front of the function (-0.4) indicates a reflection over the x-axis.

Translated 2 units left: The "-2" inside the square root indicates a translation of 2 units to the right.

Compressed by a factor of 0.4: The coefficient "0.4" in front of the square root indicates a vertical compression by a factor of 0.4.

Translated 2 units down: There is no direct indication of a vertical translation in the equation, so this transformation is not applicable.

Therefore, the correct descriptions of the graph of the transformed function compared with the parent function are:

Reflected over the x-axis

Translated 2 units right

Compressed by a factor of 0.4