Write an equation for a sine function and for a cosine function. sine:
vertical shift - 3
horizontal shift - 0
amplitude - 2
period - 2pi
domain - sin(3x)

cosine:
vertical shift - -3
horizontal shift - 4
amplitude - 2
period - 2pi
domain - cos(2x + 5)

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Step-by-step explanation:

f(x) = A sin (Bx - C) + D

amplitude = |A|

period =

phase shift =

vertical shift = D

A

amplitude of 3 is given so  3 = |A| → A = ± 3, since it is stated that this is a positive function, then A = 3

B

period of 6π is given so

C

D

vertical shift of -1 is given so -1 = D

Now, substitute the values of A, B, C, and D into the formula (above):

Next, solve when x = 2π

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

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step-by-step explanation:

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