# Algebra Examples

Describe the Transformation
Step 1
The parent function is the simplest form of the type of function given.
Step 2
The transformation from the first equation to the second one can be found by finding , , and for each equation.
Step 3
Find , , and for .
Step 4
Find , , and for .
Step 5
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: None
Step 6
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.
Vertical Shift: None
Step 7
The sign of describes the reflection across the x-axis. means the graph is reflected across the x-axis.
Reflection about the x-axis: None
Step 8
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 Stretch: Stretched
Step 9
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: None
Vertical Stretch: Stretched
Step 10