Features of Periodic Functions (NCVA)

Front

What is a periodic function?

Back

A periodic function is a function that repeats its values at regular intervals or periods. The smallest positive period is called the fundamental period.

Front

What is the amplitude of a periodic function?

Back

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

Front

How do you determine the midline of a periodic function?

Back

The midline of a periodic function is the horizontal line that runs through the middle of the graph, calculated as the average of the maximum and minimum values of the function.

Front

What is the equation of the midline for a function with a maximum of 1 and a minimum of -5?

Back

The equation of the midline is y = (1 + (-5))/2 = -2.

Front

What is the period of a periodic function?

Back

The period of a periodic function is the length of one complete cycle of the function, after which the function values repeat.

Front

How do you find the period of a sine function given its equation?

Back

The period of a sine function in the form y = a sin(bx) is calculated as 2π/|b|.

Front

What is the relationship between the amplitude and the vertical stretch of a periodic function?

Back

The amplitude indicates the vertical stretch of the function; a larger amplitude means the function stretches further from the midline.

Front

What is the effect of changing the midline on the graph of a periodic function?

Back

Changing the midline shifts the entire graph vertically without affecting the shape or period of the function.

Front

What is the difference between the amplitude and the period of a periodic function?

Back

Amplitude measures the height of the peaks from the midline, while the period measures the length of one complete cycle of the function.

Front

How can you identify the amplitude from a graph of a periodic function?

Back

The amplitude can be identified by measuring the distance from the midline to the highest or lowest point of the graph.