# State the equation: Vertical compression by a factor of -2/3, reflection in the x-axis and a vertical shift up 15 of the parent function f(x)=sinx Explain please

Begin with `f(x)=sinx` .

(1) A vertical compression of 2/3 is achieved by multiplying the function by 2/3. This reduces the amplitude by a factor of 2/3.

Thus the leading coefficient is 2/3.

(2) A reflection in the x-axis is achieved by multiplying f(x) by -1.

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Begin with `f(x)=sinx` .

(1) A vertical compression of 2/3 is achieved by multiplying the function by 2/3. This reduces the amplitude by a factor of 2/3.

Thus the leading coefficient is 2/3.

(2) A reflection in the x-axis is achieved by multiplying f(x) by -1.

Thus the leading coefficient is now -2/3.

(3) A vertical translation (shift) up of 15 units is achieved by adding 15 to f(x).

Therefore, the required function is `f(x)=-2/3sinx+15` .

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