# Precalculus Examples

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

Find the amplitude .

Amplitude:

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:

Reduce the expression by cancelling the common factors.

Factor out of .

Period:

Cancel the common factors.

Factor out of .

Period:

Cancel the common factor.

Period:

Rewrite the expression.

Period:

Period:

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:

Multiply the numerator by the reciprocal of the denominator.

Phase Shift:

Multiply .

Multiply and .

Phase Shift:

Multiply by .

Phase Shift:

Phase Shift:

Phase Shift:

Find the vertical shift .

Vertical Shift:

List the properties of the trigonometric function.

Amplitude:

Period:

Phase Shift: ( to the right)

Vertical Shift: