Transforming Polynomial Functions

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

• x² + 2

• x² - 2

• (x + 2)²

• (x - 2)²

What are the transformations?
y=3(x-4)²?

• horz shift right 4, vert stretch by a factor of 3

• horz shift left 4, vert stretch by a factor of 3

• horz shift right 4, vert stretch by a factor of 1/3

• horz shift right 4, vert shift up 3

Describe the transformation of y = f(x) for the new function
f(x) = ⅔(x - 7)² 

• Shrink of ⅔
  Right 7

• Shrink of ⅔
  Left 7

• Stretch of ⅔
  Right 7

• Stretch of ⅔
  Left 7

Describe the transformation of y = f(x) for the new function
f(x) = 5x² + 2

• Stretch of 5
  Up 2

• Shrink of 5
  Up 2

• Stretch of 5
  Down 2

• Shrink of 5
  Down 2

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

• vertical shrink by a factor of 1/4,translation down 2 units

• vertical shrink by a factor of 1/4,translation right 2 units

• vertical stretch by a factor of 1/4,translation down 2 units

• vertical stretch by a factor of 1/4,translation right 2 units

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

Describe the transformation of the graph  y = - ½(x + 4)³ - 1

• Left 4 and Down 1

• Reflected x-axis, Down 1, Left 4, Vertically Shrunk by a factor of 1/2

• Reflected x-axis, Down 1, Right 4, Vertically Shrunk by 1/2

• Reflected x-axis, Up 1, Right 4, Vertically Shrunk by a factor of 1/2

• Vertical compression by a factor of 2, and shifted left by 4 units

• Reflected over the x-axis, vertical stretch by a factor of 2, and shifted up 4 units.

• Reflected over the y-axis by a factor of 2, and shifted up by 4 units.

• None

What transformations has the function undergone?

• reflect over y, vertical compress by 2, right 5, up 1

• reflect over x, horizontal compression by 2, left 5, up 1

• reflect over x, vertical stretch by 2, right 5, up 1

• reflect over y, horizontal stretch by -2, right 5, up 1

• Vertical compression by a factor of 2, and shifted left by 4 units

• Reflected over the x-axis, vertical stretch by a factor of 2, and shifted up 4 units.

• Reflected over the y-axis by a factor of 2, and shifted up by 4 units.

• None