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: Up 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: Reflected

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: Compressed

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: Up Units

Reflection about the x-axis: Reflected

Vertical Compression: Compressed

Describe the Transformation g(x)=-|x-4|+6