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PLEASE HELP!!!!!!!!!!!!

Write the equation of the transformed graph of sine with period that has been shifted horizontally to the right 3 units, has an amplitude of 4, and has been flipped across the x-axis

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rokettojanpu

This is your generic run-of-the-mill sinusoidal function:

f(x) = sin(x)

This is the same sine function but with a phase shift of 3 units to the right:

f(x) = sin(x-3)

This is the sine function but with an amplitude of 4 units:

f(x)  = 4sin(x)

This is the sine function but flipped across the x-axis:

f(x) = -sin(x)

Combine all these transformations to get:

f(x) = -4sin(x-3)

nutanraj654

We have the function, f (x) = sinx

It is required to form a function with a period π, shifted vertically 3 units upwards, and having amplitude = 3/4

Now, as we know, 'If a function f(x) has the period P, then f(bx) will have period '.p/[b].

Since the new function needs to have period π, that is the value P/[b] = π i.e.

So, b= 2 implies the new function is f(x) = sin(2x)

Further, as the function needs to be vertically shifted 3 units upwards, we get a new function, f(x) = sinx(2) +3

Finally, the amplitude of the function must be 3/4, this means that the maximum and minimum value of the function is 3/4 and -3/4.

This gives us the transformed final function is f(x) = 3/4 sin(2x)+3.

What causes a horizontal shift right?

Given a function f, a new function g(x)=f(x−h), where h is a constant, is a horizontal shift of the function f. If h is positive, the graph will shift right.

Learn more about horizontal shift right at

https://brainly.com/question/1638409

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