period and amplitude calculator

period and amplitude calculator: Uncategorized
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Because the coefficient of x is 1, the graph should have a period of , but this graph has a period of . Remember to check specific points like . Finally, observe that the graph shows two cycles and that one entire cycle is contained in the interval . Since , the value of b could be . So the only change to the graph of  is the vertical stretch. The period of the graph is , as is the period of . The graph passes through the origin, so the function could have the form , but not . The correct answer is C. Given any function of the form  or , you know how to find the amplitude and period and how to use this information to graph the functions. Any one full pattern in the graph is called a cycle, and the length of an interval over which a cycle occurs is called the period. The value of b is , so the graph has a period of . A) Incorrect. and are called Periodic Functions. Determine a function of the form  or  whose graph is shown below. A = 1, B = 1, C = 0 and D = 0. The effect of multiplying  by 2 is to stretch the graph vertically by a factor of 2. Remember to check specific points like . For the last example, you would use, When the only change is a vertical stretch, compression, or flip, the, you saw that a negative sign on the outside (a negative value of, One last hint: besides trying to figure out the overall effect of the value of, Which of the following options is the graph of, Given a graph of a sine or cosine function, you also can determine the amplitude and period of the function. We used the variable  previously to show an angle in standard position, and we also referred to the sine and cosine functions as  and . In the next example, you will see a variation that you have not seen before. The effect of the negative sign on the inside is to replace x-values by their opposites. D) Incorrect. Some functions (like Sine and Cosine) repeat forever So the graph of  gets reflected over the x-axis. The faster it bounces the more it "Hertz". One complete cycle is shown, for example, on the interval, Incorrect. The period of  is , and the period of  is . The amplitude of a pendulum is thus one-half the distance that the bob traverses in moving from one side to the other. The correct answer is B. The negative sign on the “outside” has an additional effect: the y-values are replaced by their opposites, so the graph is also flipped over the x-axis. The length of this repeating pattern is . Log InorSign Up. The correct answer is C.   B) Incorrect. The amplitude is correct, but the period is not. However, you also need to check the orientation of the graph. At these points (where ), the value of  is 0. The value of a is , which will stretch the graph vertically by a factor of . This has the effect of shrinking the graph of  horizontally by a factor of , causing it to complete one complete cycle on the interval [0, 2]. Since the period is the length of an interval, it must always be a positive number. The period is correct, but the amplitude is not. In this function, , so this is the amplitude. The correct answer is D. Incorrect. Now we’ll look at functions of the form  and see how changes to b will affect the graph. Note the effect on the x-values of the intercepts, the high points, and the low points. Since , the function  passes through , not the origin as shown in this graph. The correct answer is B. You correctly found the amplitude and the orientation of this sine function. Correct. Regardless of the value of a, the graph must pass through the x-axis at . From this information, you can find values of, Remember that along with finding the amplitude and period, it’s a good idea to look at what is happening at, You will need to compare the graph to that of, First, observe that the graph passes through the origin, so you are looking for a function of the form, Next, observe that the maximum value of the function is 2 and the minimum is, Finally, observe that the graph shows two cycles and that one entire cycle is contained in the interval, Next, observe that the maximum value of the function is, Incorrect. The period is the length of the interval over which the one cycle runs. However, the period is incorrect. Note that in the interval , the graph of  has one full cycle. However, because the graph of cosine is symmetric about the y-axis, this has no effect at all. This is the graph of . Remember to check the value of the function at . Perhaps you confused minimum and maximum. π. In two previous examples (and) you saw that a negative sign on the outside (a negative value of a) has the effect of flipping the graph around the x-axis. So this could be the graph of . Free function amplitude calculator - find amplitude of periodic functions step-by-step This website uses cookies to ensure you get the best experience. From this information, you can find values of a and b, and then a function that matches the graph. If you multiply 0 by 4 (or anything else), you will still have a value of 0. The height of one hill (which equals the depth of one valley) is called the, Let’s look at a different kind of change to a function by graphing the function, You can find the maximum and minimum values of the function from the graph. C) The amplitude is 1, and the period is . Correct. This is the graph of a function of the form, Correct. 6 5. You have seen that changing the value of b in  or  either stretches or squeezes the graph like an accordion or a spring, but it does not change the maximum or minimum values. The correct answer is A. Given a graph of a sine or cosine function, you also can determine the amplitude and period of the function. Perhaps you recognized that the period of the graph is twice the period of , and thought that the value of b would be 2. In the interval ,  goes through one cycle while  goes through two cycles. The correct answer is D.   B) Incorrect. We’ll take the first and third columns to make part of the graph and then extend that pattern to the left and to the right. The graph shows one cycle, so the period is . Amplitude = | a | Let b be a real number.

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