Periodic Functions and Transformations

Given a graph, how do you know if it represents a periodic phenomenon?

• A graph is periodic if it has a straight line.

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

• A graph is periodic if it has no repeating pattern.

• A graph is periodic if it has random fluctuations.

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

• a person's height above ground while jumping on a trampoline

• the depth of water in a tub as it fills

• the depth of water at high or low tide

• the height of a cart in a ferris wheel as the wheel spins

Answer explanation

Filling a bathtub with water is not periodic. It rises and then stays constant. It doesn't rise and is constant again. Nothing repeats.

• Reflection across the x-axis

• Reflection across the y-axis

Answer explanation

Consider any given x-value in f(x)=sin(x). When using g(x)=-sin(x), the y-value will be the opposite. Therefore g(x) is the reflection of f(x) across the x-axis.

The period of a function is:

• how long one cycle is before the function repeats

• how high and low the function goes from the center line

Answer explanation

The Period of a periodic function goes from one peak to the next (or from any point to the next matching point).

Amplitude refers to....

• the length of the function

• how high and low the function varies from the center line.

• the difference between the max and min values

Answer explanation

Amplitude is the vertical span from the midline to either the max or min point. Amplitude is always positive because distance is positive.

The graph of a function is shown. Classify the function.

• linear

• quadratic

• periodic

• polynomial

The graph of a function is shown.

Determine the period.

Answer explanation

The graph of a function is shown.

Determine the amplitude.

Answer explanation

The graph of a function is shown.

Determine the equation of the midline.

Answer explanation

The graph of a function is shown.

Determine the frequency.