Unit 6: Periodic Functions and TrigonometryLesson 1: Exploring Periodic Data1. Use the given graph. determine the period of the function.A. 4B. -2.5C. 2D. 8For questions 2 and 3, determine whether the function is periodic. If it is, find the period.2. A. periodic; about 6B. periodic; about 3C. periodic; about 12D. not periodic3.A. periodic; about 3B. not periodicC. periodic; about 2D. periodic; about 1 1/24. Find the period and the amplitude of the periodic function.A. 1; -1B. 1; 0.5C. 2; 0.5D. 0.5; 25. 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; 4.5B. 0.05 seconds; 9C. 0.025 seconds; 9D. 0.025 seconds; 4.5Please help! I don't get this at all...

Accepted Solution

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.