What is the period of the graph

Asked by maham237 @ 10/01/2021 in Mathematics viewed by 206 People

Unit 6: Periodic Functions and Trigonometry
Lesson 1: Exploring Periodic Data

1. Use the given graph. determine the period of the function.

A. 4
B. -2.5
C. 2
D. 8

For questions 2 and 3, determine whether the function is periodic. If it is, find the period.

A. periodic; about 6
B. periodic; about 3
C. periodic; about 12
D. not periodic

A. periodic; about 3
B. not periodic
C. periodic; about 2
D. periodic; about 1 1/2

4. Find the period and the amplitude of the periodic function.

A. 1; -1
B. 1; 0.5
C. 2; 0.5
D. 0.5; 2

5. the screen below shows the graph of a sound recorded on an oscilloscope. What are the period and the amplitude? (Each unit on the t-axis equals 0.01 seconds.)

A. 0.05 seconds; 4.5
B. 0.05 seconds; 9
C. 0.025 seconds; 9
D. 0.025 seconds; 4.5

Please help! I don't get this at all...

Answered by maham237 @ 10/01/2021

Answer:

#1) A. 4; #2) A. periodic; about 6; #3) B. not periodic; #4) C. 2; 0.5; #5) A. 0.05 seconds; 4.5.

Explanation:

#1) The period of a function is essentially the amount of time it takes for the function to start all over and repeat itself. In this function, at t = 0 the graph is at 1; it curves up, back down and begins again at y=1 when t=4. This means the period goes from t=0 to t=4, so it is 4.

#2) Looking at the left side of the graph, specifically the peak at (-5, 2), we see the same peak at about (1, 2). Following the graph after that we can see that it does indeed repeat itself; this means the period goes from t= - 5 to t = 1, so it is 6.

#3) This function never repeats, so it is not periodic.

#4) This function repeats when it reaches t=2, so 2 is the period. The amplitude is the distance from the center line (of the graph, not the x-axis) to the peak. The center line would be located at about y=0.5; the peaks are at y=-1. This means the amplitude is 0.5.

#5) This function repeats every 0.05 seconds. In this case, the center line is the x-axis; the distance from it to any peak is 4.5, so 4.5 is the amplitude.

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