Periodic Functions, Midline, Period, Amplitude

Front

What is the definition of amplitude in periodic functions?

Back

Amplitude is the maximum distance from the midline to the peak (or trough) of the graph of a periodic function.

Front

How is the period of a periodic function defined?

Back

The period of a periodic function is the length of one complete cycle of the function.

Front

What is the formula to find the period of a sine or cosine function?

Back

The period of a sine or cosine function is given by the formula: Period = 2π / |b|, where b is the coefficient of x in the function.

Front

What does the midline of a periodic function represent?

Back

The midline of a periodic function represents the horizontal line that runs through the middle of the graph, indicating the average value of the function.

Front

How do you determine the midline of a sine or cosine function?

Back

The midline can be determined from the vertical shift of the function, which is the constant added or subtracted from the sine or cosine function.

Front

What is the amplitude of the function f(x) = 3sin(x)?

Back

The amplitude is 3, which is the coefficient of the sine function.

Front

If a function has a period of 4, what is the value of b in the function f(x) = sin(bx)?

Back

The value of b is π/2, since the period is calculated as 2π / |b|.

Front

What is the relationship between amplitude and the height of the peaks in a periodic function?

Back

The amplitude determines the height of the peaks and the depth of the troughs in a periodic function; it is half the distance between the maximum and minimum values.

Front

How can you find the period of a function given its graph?

Back

To find the period from a graph, measure the distance along the x-axis between two consecutive peaks (or troughs) of the function.

Front

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

Back

Changing the amplitude stretches or compresses the graph vertically, affecting the height of the peaks and the depth of the troughs.