Periodic Functions and Transformations

Front

What is the amplitude of a periodic function?

Back

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

Front

How can you determine if a graph represents a periodic phenomenon?

Back

A graph is periodic if a unique section repeats over and over again.

Front

What is the period of a periodic function?

Back

The period is the length of one complete cycle of the function, measured along the x-axis.

Front

What is the midline of a periodic function?

Back

The midline is a horizontal line that represents the average value of the function, dividing the graph into equal parts above and below.

Front

What happens to the graph of f(x)=sin(x) when transformed to g(x)=-sin(x)?

Back

The graph is reflected across the x-axis, not the y-axis.

Front

What is the formula for the amplitude of the function y = A sin(Bx + C) + D?

Back

The amplitude is |A|, where A is the coefficient of the sine function.

Front

What is the formula for the period of the function y = A sin(Bx + C) + D?

Back

The period is given by the formula \( \frac{2\pi}{|B|} \), where B is the coefficient of x.

Front

What does a vertical shift in a periodic function do?

Back

A vertical shift moves the entire graph up or down, changing the midline but not the amplitude or period.

Front

What is the effect of changing the value of A in the function y = A sin(x)?

Back

Changing A affects the amplitude of the function; larger values of A increase the height of the peaks and depth of the troughs.

Front

What is the effect of changing the value of B in the function y = A sin(Bx)?

Back

Changing B affects the period of the function; larger values of B decrease the period, resulting in more cycles in a given interval.