Precalculus Examples

Describe the Transformation
,
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
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