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Let f(x)=sin(x) and g(x)=-1/2f(x+2)-3

User Frogcjn
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Ok, so

We got the initial function:

f ( x ) = sin ( x )

And we got a function g which make some changes to the function f.

g (x) = -1/2 f ( x + 2 ) - 3

So, we're going to analyze each part.

For example, if we have a function f, f(x) and we do the following:

f ( x + 2 ), we are doing a horizontal shift to the left.

If we multiply the last function by 1/2, we are doing a vertical compression. (1/2<1). And we obtain: (1/2) f ( x + 2 )

If we multiply the function by -1, we do a reflection over x-axis. So, it's a vertical reflection. And we obtain: (-1/2) f ( x + 2 )

And finally, If we change the last function to this new one:

(-1/2) f ( x + 2 ) - 3 , We are doing a vertical shift down.

User Rahul Dasgupta
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