Section 13 - 1: Periodic Relationships

Section 13 - 1: Periodic Relationships

Graphing the relationships of periodic functions.

Multiple Choice

Which of the following events is repetitive in the real world?

• A year

• Your birthday

• The hands on a clock

• All of the above

Periodic Relationships

• A relationship the repeats in the same pattern over the same amount of time.

• Years increase in numbers but repeat the same days.

• The clock repeats itself every hour but it does not stay the same time.

Key Components to ANY Periodic Relation

• Amplitude - identifies the highest and lowest output values.

• Midline - What the amplitude is centered around.

• Period - the interval of time that a relation takes to complete one cycle or rotation. Think a year here...the period would be 365 days.

Finding Amplitude

• Find the highest y - output and the lowest output.

• Calculate the distance between the highest and lowest values.

• Divide it by two...this is the amplitude.

• (2 - (-2)) = 4...4/2 = 2. The amplitude is 2.

Finding Period

• You can start at one of three places; a highest point, a lowest point, or a zero.

• Find the x - value at that point. Let's start at the coordinate point (-3, 2) this would be a "highest point." The x - value is -3.

• Follow the function until you reach the SAME y - value that you started at. You will use that x - value as the ending point. The point (1, 2) would be the NEXT, same y - value. The x - value is 1.

Finding Period

• The distance between the x - values is the period.

• 1 - (-3) = 4; the period is 4 units.

• You can also simply count!

Multiple Choice

Which of the following is the amplitude and period of the function?

• Amplitude: 3 units

  Period: 6 units

• Amplitude: -3 units

  Period: 6 units

• Amplitude: 6 units

  Period: 3 units

• Amplitude: -4 units

  Period: 3 units

Multiple Choice

Is the following periodic?

• Yes

• No

Multiple Choice

Is the following function periodic?

• yes

• no

Multiple Choice

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

• the range of the function

Multiple Choice

What is the period of the function?

• 4

• 2

• 3

• 5

Multiple Choice

The __________ represents half the distance between the max and min of a sine or cosine graph. 

• Period
• Frequency
• Extreme Values
• Amplitude

Multiple Choice

Find the amplitude of the function.

• 3

• 4

• π/4

• 6