Transformation of Polynomial Functions

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 is f(x)=x^2, then the red must be

• g(x)=x²-5

• g(x)=x²+5

• g(x)=(x-5)²

• g(x)=(x+5)²

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

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

Shape Change: ​ (a)  

Horizontal Change ​ (b)  

Vertical Change: ​ (c)  

Parent Function: ​ (d)  

• Flip

• Vertical Stretch

• Horizontal Stretch

• Left 3

• Right 3

• Right 2

• Up 2

• Down 2

• Polynomial: Cubic

• Quadratic

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

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

• y = x³

• reflect and narrow

• left

• 1

• down

• reflect and flatten

• right

• up

• flatten

• narrow

Tags

CCSS.HSF.BF.B.3

• Flip

• Vertical Compression

• Same as

• Vertical Stretch

• Horizontal Stretch

• Horizontal Compression

• (-4,-1)

• (4,1)

Tags

CCSS.HSF.BF.B.3

Describe the transformation(s) in the following function.

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