Explanation Given: The figure 26(B) By observing the given figure we know that it is a sine function To obtain the sine function from its graph, we need to identify the following parameters. i. Period : The period (B = 2 π ω ) of a sine function is the length of one cycle of the curve. A standard sine function y = sin( x ) has a period of 2 π . ii. Amplitude : The amplitude, A, is the distance from the midpoint to the highest or lowest point of the function. The standard sine function y = sin( x ) has an amplitude of 1 iii. Shift: The horizontal shift C is obtained by determining the change being made to the x -value. The easiest way to determine horizontal shift is to determine by how many units the "starting point" (0, 0) of a standard sine curve, y = sin( x ), has moved to the right or left. Meanwhile, The vertical shift D is obtained by determining the change being made to the y -value. The easiest way to determine vertical shift is to determine by how many units the "starting point" (0, 0) of a standard sine curve, y = sin( x ), has moved to the up or down. From the values of the parameters mentioned above, the given sine function can be written as follows, y = A sin ( B ( x − C ) ) + D Calculation: Description y = A sin ( B ( x − C ) ) + D Step 1: From the given figure we know the value of the following i. Period (B = 2 π ω ): The curve completes one full cycle from x = − π 3 to x = π . ii. Amplitude: The distance from the midpoint of the graph to the highest point is 2 iii. Phase shift: The "starting point" (0, 0) of a standard sine curve, y = sin( x ), has moved to the left by ( π 3 ) units. Therefore the horizontal shift is ( π 3 ) . The graph has not moved up or down, so the vertical shift is 0

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ISBN: 9781319055844

Author: FRANZOSA

Publisher: VST

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Chapter 1.4, Problem 40E

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A function that would have a graph as in the given figure

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Chapter 1.4, Problem 39E

Chapter 1.4, Problem 41E

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Ch. 1.1 - Prob. 1PQ Ch. 1.1 - Prob. 2PQ Ch. 1.1 - Prob. 3PQ Ch. 1.1 - Prob. 4PQ Ch. 1.1 - Prob. 5PQ Ch. 1.1 - Prob. 6PQ Ch. 1.1 - Prob. 7PQ Ch. 1.1 - Prob. 8PQ Ch. 1.1 - Prob. 9PQ Ch. 1.1 - Prob. 10PQ

Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E Ch. 1.1 - Prob. 11E Ch. 1.1 - Prob. 12E Ch. 1.1 - Prob. 13E Ch. 1.1 - Prob. 14E Ch. 1.1 - Prob. 15E Ch. 1.1 - Prob. 16E Ch. 1.1 - Prob. 17E Ch. 1.1 - Prob. 18E Ch. 1.1 - Prob. 19E Ch. 1.1 - Prob. 20E Ch. 1.1 - Prob. 21E Ch. 1.1 - Prob. 22E Ch. 1.1 - Prob. 23E Ch. 1.1 - Prob. 24E Ch. 1.1 - Prob. 25E Ch. 1.1 - Prob. 26E Ch. 1.1 - Prob. 27E Ch. 1.1 - Prob. 28E Ch. 1.1 - Prob. 29E Ch. 1.1 - Prob. 30E Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 32E Ch. 1.1 - Prob. 33E Ch. 1.1 - Prob. 34E Ch. 1.1 - Prob. 35E Ch. 1.1 - Prob. 36E Ch. 1.1 - Prob. 37E Ch. 1.1 - Prob. 38E Ch. 1.1 - Prob. 39E Ch. 1.1 - Prob. 40E Ch. 1.1 - Prob. 41E Ch. 1.1 - Prob. 42E Ch. 1.1 - Prob. 43E Ch. 1.1 - Prob. 44E Ch. 1.1 - Prob. 45E Ch. 1.1 - Prob. 46E Ch. 1.1 - Prob. 47E Ch. 1.1 - Prob. 48E Ch. 1.1 - Prob. 49E Ch. 1.1 - Prob. 50E Ch. 1.1 - 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A function that would have a graph as in the given figure

Solution Summary: The author explains that the given graph is a sine function. To obtain the function from its graph, we need to identify the following parameters: period, amplitude, and vertical shift.

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A function that would have a graph as in the given figure

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Chapter 1 Solutions