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The graph shown below is one period of a function of the form $y = a \sin(k(x - b))$. Determine the function. y =

          The graph shown below is one period of a function of the form $y = a \sin(k(x - b))$. Determine the function.
y =
        
The graph shown below is one period of a function of the form y = a sin(k(x - b)). Determine the function.
y =

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Precalculus with Limits
Precalculus with Limits
Ron Larson 2nd Edition
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The graph shown below is one period of a function of the form y=asin(k(x-b)). Determine the function. y=The graph of one complete period of a cosine curve is given. (a) Find the amplitude, period, and horizontal shift. (Assume the absolute value of the horizontal shift is less than the period.) amplitude period horizontal shift (b) Write an equation that represents the curve in the form y=acos(k(x-b)). y=The graph shown below is one period of a function of the form y=asin(k(x-b)). Determine the function. y= The graph shown below is one period of a function of the form y = a sin(k(x -- b)). Determine the function. y K1 kI 3 5T 3T TT TT 8 4 8 2 8 4 18 8 5
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Transcript

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00:01 Okay, so we want to answer a few questions about this graph and then write the equation.
00:07 So first up is amplitude.
00:11 Amplitude is the highest point the graph reaches.
00:14 In this case, it's positive one -half.
00:19 The period of this graph, well, we can see one full curve from negative pi over three to positive to pi over three.
00:30 So that's 3 pi over 3 in length or just pi.
00:37 Horizontal shift, that's otherwise known as the phase shift, that tells me my graph isn't starting at 0.
00:46 In this case, it's starting at negative pi over 3.
00:53 Now i want to write the equation.
00:57 So my equation, let me just get the letters that you're, teacher uses, right? okay, so a is the amplitude.
01:09 We have that.
01:11 K is what we call the frequency.
01:13 We don't have that...
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