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 center line (midline) to the peak (maximum) or trough (minimum) of the graph.

Front

Back

Reflection across the x-axis.

Front

What is the period of the sine and cosine functions?

Back

The period of the sine and cosine functions is 2π.

Front

What does a vertical shift do to the graph of a periodic function?

Back

A vertical shift moves the entire graph up or down without changing its shape or period.

Front

What is the effect of a horizontal shift on the graph of a periodic function?

Back

A horizontal shift moves the graph left or right, affecting the starting point of the function but not its shape or period.

Front

What is the difference between a reflection across the x-axis and a reflection across the y-axis?

Back

A reflection across the x-axis flips the graph over the x-axis, while a reflection across the y-axis flips the graph over the y-axis.

Front

Which real-life situation can NOT be represented by a periodic function?

Back

The depth of water in a tub as it fills.

Front

What is the equation of the function if the graph shows a cosine function with a vertical shift down by 1 and a vertical stretch by a factor of 2?

Back

Front

What does the term 'frequency' refer to in periodic functions?

Back

Frequency refers to the number of cycles a periodic function completes in a unit interval, typically measured in cycles per unit time.