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Sinusoidal Function Parameters (2 Params) - Function to Parameters

Level 1

The topics in this unit focus on understanding how transformations change functions and the effects of stretch, compression, reflection, and moving the vertex. Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

Sinusoidal Function Parameters (2 Params) - Function to Parameters Worksheet

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Sinusoidal Function Parameters (2 Params) - Function to Parameters
1
What are the phase shift and amplitude of this sinusoidal function?
A LaTex expression showing f(x) = 5 over 7 \cos (8 over 2 x+6 over 5 Pi )+2 over 11
a A LaTex expression showing \text{Amplitude } = 5 over 7 \\\text{Phase Shift } = -6 over 5 Pi \text{ right} \\
b A LaTex expression showing \text{Amplitude } = 6 over 5 \\\text{Phase Shift } = 5 over 7 Pi \text{ left} \\
c A LaTex expression showing \text{Amplitude } = 5 over 7 \\\text{Phase Shift } = 6 over 5 Pi \text{ left} \\
d A LaTex expression showing \text{Amplitude } = 5 over 7 \\\text{Phase Shift } = 6 over 5 \text{ left} \\
2
What are the phase shift and amplitude of this sinusoidal function?
A LaTex expression showing f(x) = 6 over 3 \cos (8 over 11 Pi x+6 over 5 Pi )+5 over 2
a A LaTex expression showing \text{Amplitude } = 6 over 5 \\\text{Phase Shift } = 6 over 3 Pi \text{ left} \\
b A LaTex expression showing \text{Amplitude } = 6 over 3 \\\text{Phase Shift } = -6 over 5 Pi \text{ right} \\
c A LaTex expression showing \text{Amplitude } = 6 over 3 \\\text{Phase Shift } = 6 over 5 \text{ left} \\
d A LaTex expression showing \text{Amplitude } = 6 over 3 \\\text{Phase Shift } = 6 over 5 Pi \text{ left} \\
3
What are the amplitude and phase shift of this sinusoidal function?
A LaTex expression showing f(x) = 5 over 3 \sin (4 over 11 Pi x+4 over 7 )+2 over 11
a A LaTex expression showing \text{Amplitude } = 5 over 3 \\\text{Phase Shift } = 4 over 7 \text{ left} \\
b A LaTex expression showing \text{Amplitude } = 5 over 3 \\\text{Phase Shift } = 4 over 7 Pi \text{ left} \\
c A LaTex expression showing \text{Amplitude } = 5 over 3 \\\text{Phase Shift } = -4 over 7 \text{ right} \\
d A LaTex expression showing \text{Amplitude } = 5 over 3 \\\text{Phase Shift } = -4 over 7 Pi \text{ right} \\
4
What are the amplitude and phase shift of this sinusoidal function?
A LaTex expression showing f(x) = -6 over 5 \cos (6 over 3 Pi x+8 over 5 )+3 over 5
a A LaTex expression showing \text{Amplitude } = 6 over 5 \\\text{Phase Shift } = 8 over 5 Pi \text{ left} \\
b A LaTex expression showing \text{Amplitude } = 6 over 5 \\\text{Phase Shift } = 8 over 5 \text{ left} \\
c A LaTex expression showing \text{Amplitude } = 8 over 5 \\\text{Phase Shift } = -6 over 5 \text{ right} \\
d A LaTex expression showing \text{Amplitude } = 6 over 5 \\\text{Phase Shift } = -8 over 5 \text{ right} \\
5
What are the vertical shift and amplitude of this sinusoidal function?
A LaTex expression showing f(x) = 4 over 3 \cos (7 over 2 Pi x+8 over 2 )+5 over 3
a A LaTex expression showing \text{Amplitude } = 5 over 3 \\\text{Vertical Shift } = 4 over 3 \\
b A LaTex expression showing \text{Amplitude } = 4 over 3 \\\text{Vertical Shift } = 5 over 3 \\
6
What are the period and amplitude of this sinusoidal function?
A LaTex expression showing f(x) = 6 over 2 \cos (4 over 2 Pi x+8 over 11 Pi )+4 over 7
a A LaTex expression showing \text{Amplitude } = 6 over 2 \\\text{Period } = 4 over 4 \\
b A LaTex expression showing \text{Amplitude } = 6 over 2 \\\text{Period } = 4 Pi over 4 \\
c A LaTex expression showing \text{Amplitude } = 4 over 2 \\\text{Period } = 4 over 6 \\
7
What are the period and vertical shift of this sinusoidal function?
A LaTex expression showing f(x) = -2 over 3 \sin (8 over 2 x+7 over 3 Pi )+7 over 2
a A LaTex expression showing \text{Period } = 4 Pi over 8 \\\text{Vertical Shift } = 7 over 2 \\
b A LaTex expression showing \text{Period } = 4 Pi over 7 \\\text{Vertical Shift } = 8 over 2 \\
c A LaTex expression showing \text{Period } = 4 over 8 \\\text{Vertical Shift } = 7 over 2 \\
8
What are the period and vertical shift of this sinusoidal function?
A LaTex expression showing f(x) = -2 over 5 \sin (3 over 2 Pi x+6 over 3 Pi )+2 over 5
a A LaTex expression showing \text{Period } = 4 over 3 \\\text{Vertical Shift } = 2 over 5 \\
b A LaTex expression showing \text{Period } = 4 Pi over 3 \\\text{Vertical Shift } = 2 over 5 \\
c A LaTex expression showing \text{Period } = 10 over 2 \\\text{Vertical Shift } = 3 over 2 \\