Periodic Functions and Transformations

Front

What is a periodic function?

Back

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

Tags

CCSS.HSF.TF.A.4

Front

What is the period of a function?

Back

The period of a function is the length of one complete cycle of the function before it starts to repeat. For sine and cosine functions, the period is 2π.

Tags

CCSS.HSF.TF.A.4

Front

Back

Reflection across the x-axis.

Tags

CCSS.HSF-IF.C.7E

Front

What does the midline of a periodic function represent?

Back

The midline of a periodic function is the horizontal line that runs through the middle of the oscillation, representing the average value of the function.

Tags

CCSS.HSF-IF.C.7E

Front

How do you determine the amplitude of a periodic function?

Back

The amplitude is the maximum distance from the midline to the peak (or trough) of the function. It is calculated as half the distance between the maximum and minimum values.

Tags

CCSS.HSF-IF.C.7E

Front

Back

The amplitude is 3.

Tags

CCSS.HSF-IF.C.7E

Front

Back

It reflects the graph across the x-axis.

Tags

CCSS.HSF-IF.C.7E

Front

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

Back

The depth of water in a tub as it fills.

Tags

CCSS.HSF.TF.A.4

Front

Back

Tags

CCSS.HSF-IF.C.7E

Front

Back

A horizontal shift to the right by π units.

Tags

CCSS.HSF-IF.C.7E