9/18/2011
MB §6.1 Period Functions
Lesson Objectives:
• Define periodic functions.
• Recognize periodic functions.
• Identify the features of a periodic function:
– Period
– Midline
– Amplitude
The World’s Largest Ferris Wheel
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450 ft in diameter
800 passengers
32 capsules
1 rev/30 min
If you hop on this Ferris wheel, your height above the ground will be a function of time.
– H=f(t)
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9/18/2011
EX1: Values of f(t)
t (min)
0
7.5
15
22.5
30
37.5
45
52.5
60
f(t) (feet)
0
225
450
225
0
225
450
225
0
A) Graph the function.
B) What is the period of this function?
Definition of a Period
• Graphically, if any periodic function is shifted horizontally by its period, it will result in the same graph as the original.
• Symbolically, if the periodic function, f(t), has a period of length c, then f(t ‐ c) = f(t), for all values of t in the domain of f.
t (min)
0
7.5
15
22.5
30
37.5
45
52.5
60
f(t) (feet)
0
225
450
225
0
225
450
225
0
C) Where is the midline?
D) What is the amplitude?
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9/18/2011
Definition of the Midline and Amplitude
• The midline of a periodic function is the horizontal line halfway between the function’s minimum and maximum values. • The amplitude is the distance between its maximum and the midline.
EX2:
The function given below models the height, h, in feet, of the tide above (or below) mean sea level t hrs after 6 a.m.
A)Is the tide rising or falling at 7:00 a.m.?
B) When does low tide occur?
C) What is the amplitude?
D)What is the midline?
EX3: Which ones are periodic?
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