Transformations of Functions All Types

What are the transformations of this functions compared to the parent function y = √(x)?

• Shifted right 5, shifted down 2, and reflected over the x-axis

• Reflected over the x-axis, vertical stretch by a factor of 2, and shifted right 5

• Reflected over the x-axis, vertical stretch by a factor of 1/2, and shifted left 5

• Shifted right 5, shifted down 2

What are the transformations to the graph compared to the parent function y=√(x)?

• Reflected over the y-axis, shifted right 2 units and shifted up 3 units

• Reflected over the y-axis, shifted left 2 units, and shifted up 3 units

• Reflected over the x-axis,shifted left 2 units, and shifted up 3 units

• Reflected over the x-axis, shifted right 2 units, and shifted up 3 units

Describe the transformation of y = f(x) for the new function
 y = f(x) - 5

• The graph of y = f(x) was shifted to the right 5 units. 
• The graph of y = f(x) was shifted to the left 5 units. 
• The graph of y = f(x) was shifted up 5 units. 
• The graph of y = f(x) was shifted down 5 units.

Which equation describes the transformation of shifting f(x)=x² two units right?

• y = x² + 2

• y = x² - 2

• y = (x + 2)²

• y = (x - 2)²

What are the transformations?

y=3(x-4)²?

• vertical stretch by a factor of 3, horizontal shift right 4

• vertical stretch by a factor of 3, horizontal shift left 4

• vertical stretch by a factor of 1/3, horizontal shift right 4

• vertical shift up 3, horizontal shift right 4

Describe the transformation of y = f(x) for the new function

f(x) = ⅔(x - 7)²

• Vertical compression by a factor of ⅔

  Shift right 7 units

• Vertical compression by a factor of ⅔

  Shift left 7 units

• Vertical expansion by a factor of ⅔

  Shift right 7 units

• Vertical expansion by a factor of ⅔

  Shift left 7 units

Given f(x) = (x-3)² + 5.  What transformations took place from the original function f(x)?

• Left 3 and up 5
• Right 3 and down 5
• Left 3 and down 5
• Right 3 and up 5

If the blue graph is f(x) (the original function) and the red graph is the transformation, what is the equation of the red graph?

• -f(x)
• f(-x)
• f^-1(x)
• f(2x)

  The blue function is the original function f(x) = x³.  Which of the following is the correct equation for the red function, g(x)?

• g(x)=x³+1
• g(x)=x³-1
• g(x)=(x-1)³
• g(x)=(x+1)³

Identify the transformation from the graph of f(x)=x² to the graph g(x)= -(x+5)²

• reflection in x-axis

  shifted up five units

• reflection in x-axis

  shifted down five units

• reflection in x-axis

  shifted left 5 units

• reflection in x-axis

  shifted right 5 units