The correct answer is . Remember to check specific points like . Match a sine or cosine function to its graph and vice versa. In general, we have the following rule. Calculations in an Amortization Schedule Incorrect. We can see from the graph that the function  is a periodic function, and goes through one full cycle on the interval [0, ], so its period is . Sine function: period formula. Second, because  in the equation, the amplitude is 3. So . For the first three functions we have rewritten their periods with the numerator, In each case, the period could be found by dividing, There is another way to describe this effect. :) https://www.patreon.com/patrickjmt !! The value of a is 3, so the graph has an amplitude of 3. D) The amplitude is 1, and the period is . But to find the value of b, you must set the period equal to . Graph the cosine function with changes in amplitude and period. The period of the graph is , as is the period of . Notice also that the amplitude is equal to the coefficient of the function: Let’s compare the graph of this function to the graph of the sine function. By using this website, you agree to our Cookie Policy. However, in determining the graph, it appears that you switched the values of, You can use this information to graph any of these functions by starting with the basic graph of, You can also start with a graph, determine the values of. The formula for tangents and cotangents says that the regular period is π. Because the period is 2, the first cycle of the graph will have high points at  and 2. Periodic Function Formula. The formula for the period is the coefficient is 1 as you can see by the 'hidden' 1: $ … Second, because  in the equation, the amplitude is 3. Correct. Because it has been stretched vertically by this factor, the amplitude is twice as much, or 2. A)                                                                B), C)                                                                D). This is the graph of a function of the form . Notice that to the right of the, Incorrect. The “length” of this interval of x values is called the period. The length of this repeating pattern is, The graph below shows four repetitions of a pattern of length, If a function has a repeating pattern like sine or cosine, it is called a, You know from graphing quadratic functions of the form, Incorrect. You correctly found the amplitude and period of this sine function. A sinusoidal function (also called a sinusoidal oscillation or sinusoidal signal) is a generalized sine function.In other words, there are many sinusoidal functions; The sine is just one of them. The period of the graph is , as is the period of . A sinusoidal function can … Regardless of the value of, If you are using a graphing calculator, you need to adjust the settings for each graph to get a graphing window that shows all the features of the graph. Remember that along with finding the amplitude and period, it’s a good idea to look at what is happening at . For example, suppose you wanted the graph of . Perhaps you recognized that the period of the graph is twice the period of, Correct. However, the entire graph is one cycle, and the period equals . You correctly found the amplitude and period of this sine function. For tan(t/2), the value of B is 1/2, so the function will have a period of: \dfrac {\pi} {\left (\frac {1} … They had y-values of 1 and  for , and they have y-values of 4 and  for . Therefore, . This will flip the graph around the y-axis. Since , the function  passes through , not the origin as shown in this graph. It attains this minimum at the bottom of every valley. However, you also need to check the orientation of the graph. Graph the sine function with changes in amplitude and period. The minimum value for the sine function is, Incorrect. A) The amplitude is , and the period is . As the last example, , shows, multiplying by a constant on the outside affects the amplitude. Remember: The formula for the period only cares about the coefficient, $$ \color{red}{a} $$ in front of the x. The correct answer is A. This is the graph of . Which of the following functions is represented by the graph below? Regardless of the value of a, the graph must pass through the x-axis at . You may have thought of 0 as the minimum value, but the sine function takes on negative values. Second, because, Incorrect. The amplitude equals . This graph does have the shape of a cosine function. Up to this point, all of the values of b have been rational numbers, but here we are using the irrational number . Can you see a relationship between the function and the denominator in the periods? In each case, the period could be found by dividing  by the coefficient of x. The correct answer is D.   B) Incorrect. This is equal to the amplitude, as we mentioned at the start. This has the effect of taking the graph of  and stretching it vertically by a factor of 4. You will need to compare the graph to that of  or  to see if, in addition to any stretching or shrinking, there has been a reflection over the x-axis. However, the period is incorrect. Combine these three pieces of information. The effect of the negative sign on the inside is to replace x-values by their opposites. This is the graph of a function of the form, Correct. The correct answer is D.   D) Correct. Example: Using the RATE() formula in Excel, the rate per period (r) for a Canadian mortgage (compounded semi-annually) of $100,000 with a monthly payment of $584.45 amortized over 25 years is 0.41647% calculated using r=RATE(25*12,-584.45,100000).The annual rate is calculated to be 5.05% using the formula i=2*((0.0041647+1)^(12/2)-1).. The function hcontains all the information about how the period of a pendulum depends on its amplitude. In the interval ,  goes through one cycle while  goes through two cycles. The amplitude is 1. A periodic function repeats its values at set intervals, called periods. The correct answer is B. Because the coefficient of x is 1, the graph should have a period of , but this graph has a period of . This has the effect of taking the graph of  and shrinking it horizontally by a factor of 3. However, you have confused the effect of a minus sign on the inside with a minus sign on the outside. Since , the amplitude is 4. B) The amplitude is , and the period is . A = 1, B = 1, C = 0 and D = 0. You correctly found the amplitude and the orientation of this sine function. Note that in the interval , the graph of  has one full cycle. Notice that to the right of the y-axis you have a valley instead of a hill. These functions have the form  or , where a and b are constants. 0.02π 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. If we had looked at , the graph would have been stretched vertically by a factor of 3, and the amplitude of this function is 3. You probably multiplied, Incorrect. 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. The time period of the periodic function is given by; T = 2πω, ω is the angular frequency of the oscillating object. 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. So this could be the graph of . If you multiply 0 by 4 (or anything else), you will still have a value of 0. 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].