Sinusoidal Function Parameters (1 Param) - Graph to Function

Level 1

This math topic focuses on determining specific parameters of sinusoidal functions from their graphs. It includes analyzing amplitude, period, phase shift, and vertical shift, and matching these features to corresponding sinusoidal function equations like sine and cosine. The problems challenge the learner to decipher graphically represented trigonometric transformations (including translations and stretches) and select the correct function formula among multiple choices. The emphasis is on applying knowledge of sinusoidal transformations to interpret and formulate mathematical expressions accurately.

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Sinusoidal Function Parameters (1 Param) - Graph to Function Worksheet

Sinusoidal Function Parameters (1 Param) - Graph to Function

Which function would have a graph with this phase shift?

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a $A LaTex expression showing f(x) = \sin (x+5 over 6 )$

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

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

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

Which function would have a graph with this period?

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a $A LaTex expression showing f(x) = \sin (10 over 6 Pi x)$

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

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

d $A LaTex expression showing f(x) = \sin (11 over 6 Pi x)$

Which function would have a graph with this amplitude?

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a $A LaTex expression showing f(x) = -7\cos (x)$

b $A LaTex expression showing f(x) = 0\cos (x)$

c $A LaTex expression showing f(x) = -3\cos (x)$

d $A LaTex expression showing f(x) = 3\cos (x)$

Which function would have a graph with this phase shift?

An svg image showing a math problem

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

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

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

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

Which function would have a graph with this vertical shift?

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a $A LaTex expression showing f(x) = \sin (x)-5$

b $A LaTex expression showing f(x) = \sin (x)-2$

c $A LaTex expression showing f(x) = \sin (x)+6$

d $A LaTex expression showing f(x) = \sin (x)-3$

Which function would have a graph with this phase shift?

An svg image showing a math problem

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

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

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

d $A LaTex expression showing f(x) = \cos (x+5)$

Which function would have a graph with this period?

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a $A LaTex expression showing f(x) = \sin (6x)$

b $A LaTex expression showing f(x) = \sin (5x)$

c $A LaTex expression showing f(x) = \sin (2x)$

d $A LaTex expression showing f(x) = \sin (4x)$

Which function would have a graph with this amplitude?

An svg image showing a math problem

a $A LaTex expression showing f(x) = 4\cos (x)$

b $A LaTex expression showing f(x) = -5\cos (x)$

c $A LaTex expression showing f(x) = -3\cos (x)$

d $A LaTex expression showing f(x) = 2\cos (x)$