Translating Radical Functions

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

What kind of function is represented by the graph?

• Cube Root Function
• Cubic Function
• Polynomial Function
• Square Root Function

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. 

• 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

Name the parent function.

• cube root
• quadratic
• cubic
• square root

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.

What are the transformations of this functions compared to the parent function?

• Shifted down 2
• Shifted up 2
• Shifted left 2
• Shifted right 2

What are the transformations to the graph compared to the parent function?

• Shifted right 2, shifted up 3, and reflected over the y-axis
• Shifted left 2, shifted up 3, and reflected over the y-axis
• Shifted left 2, shifted up 3, and reflected over the x-axis
• Shifted right 2, shifted up 3, and reflected over the x-axis

How are the graphs of a function and its inverse related?

• The graphs are symmetric about the y-axis.

• The graphs are symmetric about the x-axis.

• The graphs are symmetric about the line y = x.

• The graphs are identical.

Which is an equation that shifts the graph of the function above to the left 5 units?

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