Polynomial Transformations

What are the transformations of the following polynomial from the parent function f(x)=x^3?

• Vertical compression by a factor of 2, and shifted right by 1 unit

• Reflected over the x-axis, vertical stretch by a factor of 2, and shift left by 1 unit

• Reflected over the y-axis by a factor of 2, and shifted up by 1 unit

• Reflected over the x-axis, horizontal compression by a factor of 2, and shifted down by 1 unit

Tags

CCSS.HSF.BF.B.3

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

• Left 4 and Down 1

• Reflected x-axis, Down 1, Left 4, Shrink by 1/2

• Reflected x-axis, Down 1, Left 4, Stretch by 1/2

• Reflected x-axis, Up 1, Right 4, Shrink by 1/2

Tags

CCSS.HSF.BF.B.3

If f(x) = x³ is changed to f(x) = - (x + 3)³ + 2, how is the graph transformed?

• 3 units right, 2 units up, reflected across the y-axis

• 3 units right, 2 units up, reflected across the x-axis

• 3 units left, 2 units up, reflected across the y-axis

• 3 units left, 2 units up, reflected across the x-axis

Tags

CCSS.HSF.BF.B.3

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

Tags

CCSS.HSF.BF.B.3

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

Tags

CCSS.HSF.BF.B.3

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

Tags

CCSS.HSF.BF.B.3

• y = x³

• reflect and narrow

• left

• 1

• down

• reflect and flatten

• right

• up

• flatten

• narrow

Tags

CCSS.HSF.BF.B.3

Which transformation maps the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

• a translation shifting f(x) 4 units up

• a translation shifting f(x) 4 units down

• a translation shifting f(x) 4 units to the left

• a translation shifting f(x) 4 units to the right

In the equation f(x)=1/2(x+9)²-1, what happens to the parabola?

• Reflect, horizontal compress by 1/2, left 9, down 1

• Vertical compress by 1/2, left 9, down 1

• Horizontal Compress by 1/2, right 9, down 1

• Vertical Stretch by 1/2, left 9, down 1

Describe the transformations of the graph y = (x - 3)³ -2

• Right 3, Down 2

• Left 3, Up 2

• Right 3, Up 2

• Left 3, Down 2 

Tags

CCSS.HSF.BF.B.3