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

For a better explanation, assume that is and is .

Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift.

Since the graph of the function does not have a maximum or minimum value, there can be no value for the amplitude.

Amplitude: None

The period of the function can be calculated using .

Period:

Replace with in the formula for period.

Period:

Solve the equation.

The absolute value is the distance between a number and zero. The distance between and is .

Period:

Divide by .

Period:

Period:

Period:

The phase shift of the function can be calculated from .

Phase Shift:

Replace the values of and in the equation for phase shift.

Phase Shift:

Divide by .

Phase Shift:

Phase Shift:

Find the vertical shift .

Vertical Shift:

List the properties of the trigonometric function.

Amplitude: None

Period:

Phase Shift: ( to the right)

Vertical Shift:

Describe the Transformation y=tan(x)