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Sinusoidal Function Parameters (4 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 (4 Params) - Function to Parameters Worksheet

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Sinusoidal Function Parameters (4 Params) - Function to Parameters
1
What are the period, amplitude, vertical shift, and phase shift of this sinusoidal function?
A LaTex expression showing f(x) = -3 over 5 \sin (6 over 5 Pi x+3 over 2 )+6 over 11
a A LaTex expression showing \text{Amplitude } = 3 over 5 \\\text{Period } = 10 over 6 \\\text{Phase Shift } = -3 over 2 \text{ right} \\\text{Vertical Shift } = 6 over 11 \\
b A LaTex expression showing \text{Amplitude } = 3 over 5 \\\text{Period } = 10 over 6 \\\text{Phase Shift } = 3 over 2 \text{ left} \\\text{Vertical Shift } = 6 over 11 \\
c A LaTex expression showing \text{Amplitude } = 3 over 5 \\\text{Period } = 10 over 6 \\\text{Phase Shift } = 3 over 2 Pi \text{ left} \\\text{Vertical Shift } = 6 over 11 \\
d A LaTex expression showing \text{Amplitude } = 3 over 2 \\\text{Period } = 10 over 6 \\\text{Phase Shift } = -3 over 5 \text{ right} \\\text{Vertical Shift } = 6 over 11 \\
2
What are the vertical shift, period, amplitude, and phase shift of this sinusoidal function?
A LaTex expression showing f(x) = 3 over 7 \cos (5 over 2 Pi x+6 over 7 Pi )+3 over 11
a A LaTex expression showing \text{Amplitude } = 3 over 7 \\\text{Period } = 4 over 5 \\\text{Phase Shift } = 6 over 7 Pi \text{ left} \\\text{Vertical Shift } = 3 over 11 \\
b A LaTex expression showing \text{Amplitude } = 3 over 7 \\\text{Period } = 4 over 5 \\\text{Phase Shift } = 3 over 11 Pi \text{ left} \\\text{Vertical Shift } = 6 over 7 \\
c A LaTex expression showing \text{Amplitude } = 5 over 2 \\\text{Period } = 14 over 3 \\\text{Phase Shift } = 6 over 7 Pi \text{ left} \\\text{Vertical Shift } = 3 over 11 \\
d A LaTex expression showing \text{Amplitude } = 3 over 7 \\\text{Period } = 4 over 5 \\\text{Phase Shift } = 6 over 7 \text{ left} \\\text{Vertical Shift } = 3 over 11 \\
3
What are the amplitude, phase shift, period, and vertical shift of this sinusoidal function?
A LaTex expression showing f(x) = -8 over 11 \cos (8 over 5 x+7 over 5 Pi )+8 over 3
a A LaTex expression showing \text{Amplitude } = 7 over 5 \\\text{Period } = 10 Pi over 8 \\\text{Phase Shift } = -8 over 11 Pi \text{ right} \\\text{Vertical Shift } = 8 over 3 \\
b A LaTex expression showing \text{Amplitude } = 8 over 11 \\\text{Period } = 6 Pi over 8 \\\text{Phase Shift } = 7 over 5 Pi \text{ left} \\\text{Vertical Shift } = 8 over 5 \\
c A LaTex expression showing \text{Amplitude } = 8 over 11 \\\text{Period } = 10 Pi over 8 \\\text{Phase Shift } = 7 over 5 Pi \text{ left} \\\text{Vertical Shift } = 8 over 3 \\
d A LaTex expression showing \text{Amplitude } = 8 over 11 \\\text{Period } = 10 Pi over 7 \\\text{Phase Shift } = 8 over 5 Pi \text{ left} \\\text{Vertical Shift } = 8 over 3 \\
4
What are the phase shift, amplitude, vertical shift, and period of this sinusoidal function?
A LaTex expression showing f(x) = -2 over 3 \sin (3 over 5 x+3 over 7 )+7 over 5
a A LaTex expression showing \text{Amplitude } = 2 over 3 \\\text{Period } = 10 Pi over 3 \\\text{Phase Shift } = -3 over 7 \text{ right} \\\text{Vertical Shift } = 7 over 5 \\
b A LaTex expression showing \text{Amplitude } = 3 over 5 \\\text{Period } = 6 Pi over 2 \\\text{Phase Shift } = -3 over 7 \text{ right} \\\text{Vertical Shift } = 7 over 5 \\
c A LaTex expression showing \text{Amplitude } = 2 over 3 \\\text{Period } = 10 Pi over 3 \\\text{Phase Shift } = 3 over 7 \text{ left} \\\text{Vertical Shift } = 7 over 5 \\
d A LaTex expression showing \text{Amplitude } = 2 over 3 \\\text{Period } = 10 Pi over 3 \\\text{Phase Shift } = 7 over 5 \text{ left} \\\text{Vertical Shift } = -3 over 7 \\
5
What are the vertical shift, period, amplitude, and phase shift of this sinusoidal function?
A LaTex expression showing f(x) = 4 over 11 \sin (7 over 3 x+6 over 3 Pi )+7 over 5
a A LaTex expression showing \text{Amplitude } = 6 over 3 \\\text{Period } = 6 Pi over 7 \\\text{Phase Shift } = 4 over 11 Pi \text{ left} \\\text{Vertical Shift } = 7 over 5 \\
b A LaTex expression showing \text{Amplitude } = 4 over 11 \\\text{Period } = 6 Pi over 7 \\\text{Phase Shift } = 6 over 3 Pi \text{ left} \\\text{Vertical Shift } = 7 over 5 \\
c A LaTex expression showing \text{Amplitude } = 4 over 11 \\\text{Period } = 6 Pi over 7 \\\text{Phase Shift } = 6 over 3 \text{ left} \\\text{Vertical Shift } = 7 over 5 \\
d A LaTex expression showing \text{Amplitude } = 4 over 11 \\\text{Period } = 6 Pi over 7 \\\text{Phase Shift } = -6 over 3 Pi \text{ right} \\\text{Vertical Shift } = 7 over 5 \\
6
What are the period, amplitude, phase shift, and vertical shift of this sinusoidal function?
A LaTex expression showing f(x) = -5 over 7 \sin (3 over 7 x+6 over 2 Pi )+6 over 3
a A LaTex expression showing \text{Amplitude } = 5 over 7 \\\text{Period } = 6 Pi over 6 \\\text{Phase Shift } = 6 over 2 Pi \text{ left} \\\text{Vertical Shift } = 3 over 7 \\
b A LaTex expression showing \text{Amplitude } = 5 over 7 \\\text{Period } = 4 Pi over 6 \\\text{Phase Shift } = 3 over 7 Pi \text{ left} \\\text{Vertical Shift } = 6 over 3 \\
c A LaTex expression showing \text{Amplitude } = 3 over 7 \\\text{Period } = 14 Pi over 5 \\\text{Phase Shift } = 6 over 2 Pi \text{ left} \\\text{Vertical Shift } = 6 over 3 \\
d A LaTex expression showing \text{Amplitude } = 5 over 7 \\\text{Period } = 14 Pi over 3 \\\text{Phase Shift } = 6 over 2 Pi \text{ left} \\\text{Vertical Shift } = 6 over 3 \\
7
What are the vertical shift, amplitude, phase shift, and period of this sinusoidal function?
A LaTex expression showing f(x) = 7 over 2 \sin (8 over 3 Pi x+5 over 2 Pi )+6 over 3
a A LaTex expression showing \text{Amplitude } = 7 over 2 \\\text{Period } = 6 over 8 \\\text{Phase Shift } = 5 over 2 Pi \text{ left} \\\text{Vertical Shift } = 6 over 3 \\
b A LaTex expression showing \text{Amplitude } = 7 over 2 \\\text{Period } = 6 Pi over 8 \\\text{Phase Shift } = 5 over 2 Pi \text{ left} \\\text{Vertical Shift } = 6 over 3 \\
c A LaTex expression showing \text{Amplitude } = 7 over 2 \\\text{Period } = 6 over 8 \\\text{Phase Shift } = 5 over 2 \text{ left} \\\text{Vertical Shift } = 6 over 3 \\
d A LaTex expression showing \text{Amplitude } = 6 over 3 \\\text{Period } = 6 over 8 \\\text{Phase Shift } = 5 over 2 Pi \text{ left} \\\text{Vertical Shift } = 7 over 2 \\
8
What are the phase shift, period, vertical shift, and amplitude of this sinusoidal function?
A LaTex expression showing f(x) = -4 over 7 \cos (3 over 11 Pi x+4 over 5 )+2 over 5
a A LaTex expression showing \text{Amplitude } = 3 over 11 \\\text{Period } = 14 over 4 \\\text{Phase Shift } = 4 over 5 \text{ left} \\\text{Vertical Shift } = 2 over 5 \\
b A LaTex expression showing \text{Amplitude } = 2 over 5 \\\text{Period } = 22 over 3 \\\text{Phase Shift } = 4 over 5 \text{ left} \\\text{Vertical Shift } = -4 over 7 \\
c A LaTex expression showing \text{Amplitude } = 4 over 7 \\\text{Period } = 22 over 3 \\\text{Phase Shift } = 4 over 5 \text{ left} \\\text{Vertical Shift } = 2 over 5 \\
d A LaTex expression showing \text{Amplitude } = 4 over 7 \\\text{Period } = 10 over 4 \\\text{Phase Shift } = 3 over 11 \text{ left} \\\text{Vertical Shift } = 2 over 5 \\