Periodic Functions and Transformations

Front

What is a periodic function?

Back

A periodic function is a function that repeats its values at regular intervals or periods. For example, the sine and cosine functions are periodic with a period of 2π.

Front

What is the amplitude of a periodic function?

Back

The amplitude of a periodic function is the maximum distance from the midline (equilibrium position) to the peak (or trough) of the wave. It represents the height of the wave.

Front

What transformation occurs when a function is reflected across the x-axis?

Back

Front

How can you identify a periodic function from its graph?

Back

A periodic function will show a repeating pattern in its graph. The intervals between peaks and troughs will be consistent.

Front

What is the period of the sine function?

Back

The period of the sine function is 2π, meaning it completes one full cycle every 2π units along the x-axis.

Front

What is the difference between sine and cosine functions?

Back

Sine and cosine functions are both periodic, but they are phase-shifted by π/2. The sine function starts at 0, while the cosine function starts at its maximum value.

Front

What is a transformation in the context of functions?

Back

A transformation is an operation that alters the position, size, or shape of a graph. Common transformations include translations, reflections, stretches, and compressions.

Front

What does it mean to translate a function vertically?

Back

Front

What is the effect of a horizontal stretch on a periodic function?

Back

Front

What is the equation of a cosine function with an amplitude of 2 and a vertical shift of -1?

Back