# Algebra Examples

The parent function is the simplest form of the type of function given.

For a better explanation, assume that is and is .

The transformation from the first equation to the second one can be found by finding , , and for each equation.

Find , , and for .

Find , , and for .

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: Left Units

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: Down Units

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

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: Left Units

Vertical Shift: Down Units

Reflection about the x-axis: None