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Sinusoidal Function Parameters (3 Params) - Graph to Function

Level 1

This math topic focuses on identifying sinusoidal function parameters from given graphs. It targets three primary transformations of sinusoidal functions: vertical shifts, phase shifts, and amplitude changes. Each problem presents a sinusoidal graph with one altered parameter and asks to determine which function, out of several choices, correctly represents the transformation shown in the graph. This allows learners to apply knowledge of sinusoidal functions transformations, specifically how changes in the function equations affect their graphical representations.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Sinusoidal Function Parameters (3 Params) - Graph to Function Worksheet

Sinusoidal Function Parameters (3 Params) - Graph to Function

Which function would have a graph with this vertical shift?

An svg image showing a math problem

a $A LaTex expression showing f(x) = -2\cos (3 over 4 Pi x)-5$

b $A LaTex expression showing f(x) = -2\cos (3 over 4 Pi x)+5$

c $A LaTex expression showing f(x) = -2\cos (3 over 4 Pi x)-4$

d $A LaTex expression showing f(x) = -2\cos (3 over 4 Pi x)-2$

Which function would have a graph with this phase shift?

An svg image showing a math problem

a $A LaTex expression showing f(x) = \sin (1 over 4 Pi x-8 over 6 Pi )+5$

b $A LaTex expression showing f(x) = \sin (1 over 4 Pi x-2 over 6 Pi )+5$

c $A LaTex expression showing f(x) = \sin (1 over 4 Pi x+3 Pi )+5$

d $A LaTex expression showing f(x) = \sin (1 over 4 Pi x+2 over 6 Pi )+5$

Which function would have a graph with this amplitude?

An svg image showing a math problem

a $A LaTex expression showing f(x) = -5\cos (2x+6 Pi )$

b $A LaTex expression showing f(x) = -4\cos (2x+6 Pi )$

c $A LaTex expression showing f(x) = -3\cos (2x+6 Pi )$

d $A LaTex expression showing f(x) = -7\cos (2x+6 Pi )$

Which function would have a graph with this vertical shift?

An svg image showing a math problem

a $A LaTex expression showing f(x) = 4\sin (1 over 2 Pi x)+3$

b $A LaTex expression showing f(x) = 4\sin (1 over 2 Pi x)+2$

c $A LaTex expression showing f(x) = 4\sin (1 over 2 Pi x)-5$

d $A LaTex expression showing f(x) = 4\sin (1 over 2 Pi x)+6$

Which function would have a graph with this phase shift?

An svg image showing a math problem

a $A LaTex expression showing f(x) = -6\sin (1 over 3 Pi x-2 over 6 Pi )$

b $A LaTex expression showing f(x) = -6\sin (1 over 3 Pi x-3 over 6 Pi )$

c $A LaTex expression showing f(x) = -6\sin (1 over 3 Pi x+5 Pi )$

d $A LaTex expression showing f(x) = -6\sin (1 over 3 Pi x-5 over 6 Pi )$

Which function would have a graph with this phase shift?

An svg image showing a math problem

a $A LaTex expression showing f(x) = \cos (1 over 2 Pi x-8 over 6 Pi )+3$

b $A LaTex expression showing f(x) = \cos (1 over 2 Pi x-5 over 6 Pi )+3$

c $A LaTex expression showing f(x) = \cos (1 over 2 Pi x+2 Pi )+3$

d $A LaTex expression showing f(x) = \cos (1 over 2 Pi x-2 over 6 Pi )+3$

Which function would have a graph with this amplitude?

An svg image showing a math problem

a $A LaTex expression showing f(x) = -3\cos (1 over 4 Pi x)+6$

b $A LaTex expression showing f(x) = 3\cos (1 over 4 Pi x)+6$

c $A LaTex expression showing f(x) = \cos (1 over 4 Pi x)+6$

d $A LaTex expression showing f(x) = 7\cos (1 over 4 Pi x)+6$

Which function would have a graph with this period?

An svg image showing a math problem

a $A LaTex expression showing f(x) = \cos (1 over 6 Pi x+2)+7$

b $A LaTex expression showing f(x) = \cos (6 over 6 Pi x+2)+7$

c $A LaTex expression showing f(x) = \cos (3 over 6 Pi x+2)+7$

d $A LaTex expression showing f(x) = \cos (11 over 6 Pi x+2)+7$