# Precalculus Examples

Describe the Transformation
,
The transformation from the first equation to the second one can be found by finding , , and for each equation.
Factor a out of the absolute value to make the coefficient of equal to .
Factor a out of the absolute value to make the coefficient of equal to .
Find , , and for .
The horizontal shift depends on the value of . When , the horizontal shift is described as:
- The graph is shifted to the left units.
- The graph is shifted to the right units.
Horizontal Shift: None
The vertical shift depends on the value of . When , the vertical shift is described as:
- The graph is shifted up units.
- The graph is shifted down units.
Vertical Shift: Up Units
The sign of describes the reflection across the x-axis. means the graph is reflected across the x-axis.
The value of describes the vertical stretch or compression of the graph.
is a vertical stretch (makes it narrower)
is a vertical compression (makes it wider)
Vertical Compression or Stretch: None
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: Up Units