Transformation of Cube Root Functions

If f(x) = ∛(x) is reflected over the x-axis, vertically compressed by a factor of 1/4, and shifted left 9, which equation is correct?

• 1/4 ∛(x + 9)

• 1/4 ∛(x - 9)

• - 1/4 ∛(x + 9)

• - 1/4 ∛(x - 9)

What transformations have occurred to get the graph of g(x) from the graph of f(x)?

• reflection over the x-axis,vertical compress by a factor of 5

• reflection over the y-axis,vertical compress by a factor of 5

• reflection over the x-axis,vertical stretch by a factor of 5

• reflection over the y-axis,vertical stretch by a factor of 5

Identify the Transformations. 

• Vertical stretch by 2 and down 4

• Horizontal compression by ½ and down 4

• Vertical stretch by 2 and up 4

• Horizontal compression by ½ and right 4

Which of the following is the graph of y = (x – 1)³ – 7?

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Compare the functions.

• The graph of g is a translation 2 units left and a reflection in the x-axis of the graph of f.

• The graph of g is a translation 3 units right and there is no reflection in the x-axis of the graph of f.

• The graph of g is a translation 4 units left and a reflection in the x-axis of the graph of f.

• The graph of g is a translation 5 units left and there is no reflection in the x-axis of the graph of f.

• The range is y ≥ 1
• It has been reflected over the x-axis
• The function has been shifted up 1 unit
• The function has been shifted up 2 units

Which equation is a cube root function that moves 3 units to the left and 7 units down from the PARENT function?

• h(x) = ∛(x + 3) - 1

• h(x) = ∛(x + 3) - 7

• h(x) = ∛(x - 7) + 1

• h(x) = ∛(x - 3)

Describe the transformations of the graph shown. 

• Shifted down 4 units, vertically compressed by a factor of 3, and shifted 6 units left. 

• Shifted down 4 units, horizontal compression by a factor of 3, and shifted 6 units left. 

• Shifted down 4 units, vertically compressed by a factor of 3, and shifted 6 units right. 

• none of the above.

Which of the facts is not true about the graph shown?

• The range is y ∈ ℝ

• The function has been shifted 6 units right.

• The function has been shifted up 1 unit

• The function has been vertically stretched by a factor of 2. 

What cube root function is transformed 2 units left, 5 units down, and 0.5 times the proportions of the parent function? *Choose 2 that apply

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