+3

Sinusoidal Function Parameters (2 Params) - Graph to Function

Level 1

This math topic involves identifying parameters of sinusoidal functions from their graphs. It covers determining vertical shifts, periods, and amplitudes of sine and cosine functions. Each question presents a graph and multiple choice answers that include various sinusoidal equations. The task is to match the correct function with the given graph attribute (shift, period, or amplitude). This practice is part of a broader study on functions, specifically focusing on transformation, composition, and inversion.

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

more

Worksheet ViewUnit

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

Sinusoidal Function Parameters (2 Params) - Graph to Function

Which function would have a graph with this vertical shift?

An svg image showing a math problem

a $A LaTex expression showing f(x) = \sin (x+8 Pi )+2$

b $A LaTex expression showing f(x) = \sin (x+8 Pi )+4$

c $A LaTex expression showing f(x) = \sin (x+8 Pi )-5$

d $A LaTex expression showing f(x) = \sin (x+8 Pi )$

Which function would have a graph with this vertical shift?

An svg image showing a math problem

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

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

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

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

Which function would have a graph with this period?

An svg image showing a math problem

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

b $A LaTex expression showing f(x) = \sin (4 over 3 Pi x+7)$

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

Which function would have a graph with this period?

An svg image showing a math problem

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

b $A LaTex expression showing f(x) = \sin (5x)+7$

c $A LaTex expression showing f(x) = \sin (3x)+7$

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

Which function would have a graph with this amplitude?

An svg image showing a math problem

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

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

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

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

Which function would have a graph with this amplitude?

An svg image showing a math problem

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

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

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

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

Which function would have a graph with this amplitude?

An svg image showing a math problem

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

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

c $A LaTex expression showing f(x) = -5\cos (x)+4$

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

Which function would have a graph with this amplitude?

An svg image showing a math problem

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

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

c $A LaTex expression showing f(x) = -3\cos (x)+5$

d $A LaTex expression showing f(x) = 4\cos (x)+5$