# Precalculus Examples

Describe the Transformation
Step 1
The parent function is the simplest form of the type of function given.
Step 2
Assume that is and is .
Step 3
The transformation from the first equation to the second one can be found by finding , , and for each equation.
Step 4
Factor a out of the absolute value to make the coefficient of equal to .
Step 5
Factor a out of the absolute value to make the coefficient of equal to .
Step 6
Find , , and for .
Step 7
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: Right Units
Step 8
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: Down Units
Step 9
The sign of describes the reflection across the x-axis. means the graph is reflected across the x-axis.
Step 10
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
Step 11
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: Right Units
Vertical Shift: Down Units