# Precalculus Examples

,

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.

In this case, which means that the graph is not shifted to the left or right.

Horizontal Shift: None

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 , which matches the transformation from to .

Reflection about the x-axis: Reflected

The graph is reflected about the y-axis when , which does not match the transformation from to .

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

In this case, the graph is vertically stretched.

Vertical Compression or Stretch: Stretched

To find the transformation, compare the two functions and check to see if there is a horizontal or vertical shift, reflection about the x-axis, and if there is a vertical stretch.

Parent Function:

Horizontal Shift: None

Vertical Shift: None

Reflection about the x-axis: Reflected

Reflection about the y-axis: None

Vertical Compression or Stretch: Stretched