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Sinusoidal Function Parameters (4 Params) - Graph to Function

Level 1

This math topic focuses on understanding and interpreting the four main parameters of sinusoidal functions through graphical analysis. Students are asked to identify which sinusoidal functions correspond to specific properties like amplitude, period, and phase shift from provided graphs. Each question provides several function options (expressed in LaTeX format), alongside graphs depicting characteristics such as amplitude changes or phase shifts, and requires students to match these characteristics to the correct sinusoidal function. This falls under a larger unit on functions involving transformation, composition, and inversion.

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

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

Sinusoidal Function Parameters (4 Params) - Graph to Function

An svg image showing a math problem

Which function would have a graph with this period?

a $A LaTex expression showing f(x) = -6\sin (1 over 2 Pi x+5)+8$

b $A LaTex expression showing f(x) = -6\sin (3 over 2 Pi x+5)+8$

Which function would have a graph with this phase shift?

An svg image showing a math problem

a $A LaTex expression showing f(x) = 4\cos (5 over 6 Pi x+1 over 6 )+7$

b $A LaTex expression showing f(x) = 4\cos (5 over 6 Pi x+8)+7$

c $A LaTex expression showing f(x) = 4\cos (5 over 6 Pi x-1 over 6 )+7$

d $A LaTex expression showing f(x) = 4\cos (5 over 6 Pi x-6 over 6 )+7$

Which function would have a graph with this amplitude?

An svg image showing a math problem

a $A LaTex expression showing f(x) = -5\cos (1 over 2 Pi x+5)+7$

b $A LaTex expression showing f(x) = -1\cos (1 over 2 Pi x+5)+7$

c $A LaTex expression showing f(x) = 4\cos (1 over 2 Pi x+5)+7$

d $A LaTex expression showing f(x) = 0\cos (1 over 2 Pi x+5)+7$

Which function would have a graph with this period?

An svg image showing a math problem

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

b $A LaTex expression showing f(x) = 7\cos (10 over 6 Pi x+3)+2$

c $A LaTex expression showing f(x) = 7\cos (5 over 6 Pi x+3)+2$

d $A LaTex expression showing f(x) = 7\cos (9 over 6 Pi x+3)+2$

Which function would have a graph with this amplitude?

An svg image showing a math problem

a $A LaTex expression showing f(x) = 4\sin (3x+6 Pi )+2$

b $A LaTex expression showing f(x) = -4\sin (3x+6 Pi )+2$

c $A LaTex expression showing f(x) = -5\sin (3x+6 Pi )+2$

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

Which function would have a graph with this amplitude?

An svg image showing a math problem

a $A LaTex expression showing f(x) = 7\cos (1 over 2 Pi x+2)+5$

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

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

d $A LaTex expression showing f(x) = 0\cos (1 over 2 Pi x+2)+5$

Which function would have a graph with this phase shift?

An svg image showing a math problem

a $A LaTex expression showing f(x) = 2\cos (3x+4 over 6 )+6$

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

c $A LaTex expression showing f(x) = 2\cos (3x+4)+6$

d $A LaTex expression showing f(x) = 2\cos (3x-4 over 6 )+6$

Which function would have a graph with this amplitude?

An svg image showing a math problem

a $A LaTex expression showing f(x) = -3\sin (2x+7 Pi )+6$

b $A LaTex expression showing f(x) = 0\sin (2x+7 Pi )+6$

c $A LaTex expression showing f(x) = 5\sin (2x+7 Pi )+6$

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