Algebra Examples

Describe the Transformation
The parent function is the simplest form of the type of function given.
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: Right Units
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: None
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
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
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: None
Reflection about the x-axis: None
Vertical Stretch: Stretched
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