Label each of the following graphs with the appropriate function. Calculator should be set to radians. Window Xscl should be set to pi. The amplitude equals:

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Presentation transcript:

Label each of the following graphs with the appropriate function. Calculator should be set to radians. Window Xscl should be set to pi. The amplitude equals: Identify the amplitude for each graph. Then, compare the amplitude to the equation. Can you find a relationship between the amplitude and the equation? Compare the related sine and cosine functions and their respective graphs. What is the difference between a sine function and the similar cosine function? Amplitude is the |A|, where A = ½ A = 1 A = 2 A = 3

Label each of the following graphs with the appropriate function. Calculator should be set to radians. Window Xscl should be set to pi. Now, look at the related functions and their respective graphs. Find the period (the interval required for the graph to complete one cycle, move through positive and negative values) for each graph? Compare the period and the equation for each. Can you find a relationship between the period and the equation? Period is, where

Label each of the following graphs with the appropriate function. Calculator should be set to radians. Window Xscl should be set to pi. The phase shift of a function is the horizontal translation or shift. Look at the functions and their respective graphs. How much did each shift in terms of pi? Now, compare the shifts with the equations. Can you find a relationship? Phase shift is, where If c > 0, shifts left. If c < 0, shifts right.

Label each of the following graphs with the appropriate function. Calculator should be set to radians. Window Xscl should be set to pi. The midline is the new horizontal axis reference line about which the graph oscillates after a vertical shift. Look at the functions and their respective graphs. How much did each shift vertically? Now, compare the shifts with the equations. Can you find a relationship? Write the equation of the midline as y = ? for the graphs not centered about the x-axis. Vertical shift is d, where Midline is vs = 3 vs = -3 vs = 1 vs = -1

Amplitude is the |A|, where Period is, where Phase shift is, where If c > 0, shifts left. If c < 0, shifts right. Vertical shift is d, where Midline is Identify the amplitude, period, phase shift, vertical shift, and equation of the midline.