The parent function is the simplest form of the type of function given.

Use the Binomial Theorem.

Simplify each term.

Multiply by .

Raise to the power of .

Multiply by .

Raise to the power of .

For a better explanation, assume that is and is .

The transformation being described is from to .

The horizontal shift depends on the value of . The horizontal shift is described as:

– The graph is shifted to the left units.

– The graph is shifted to the right units.

Horizontal Shift: Right Units

The vertical shift depends on the value of . The vertical shift is described as:

– The graph is shifted up units.

– The graph is shifted down units.

In this case, which means that the graph is not shifted up or down.

Vertical Shift: None

The graph is reflected about the x-axis when .

Reflection about the x-axis: None

The graph is reflected about the y-axis when .

Reflection about the y-axis: None

Compressing and stretching depends on the value of .

When is greater than : Vertically stretched

When is between and : Vertically compressed

Vertical Compression or Stretch: None

Compare and list the transformations.

Parent Function:

Horizontal Shift: Right Units

Vertical Shift: None

Reflection about the x-axis: None

Reflection about the y-axis: None

Vertical Compression or Stretch: None

Describe the Transformation y=(x-10)^3