What have I done wrong? [Trigonometry]

[DeBrogliez]

Hello everyone,

I have a question in Mathematics.

Considering the general form of a cosine function to be:

I have the following function:

The following transformations are performed to map f(t) into g(t):

Horizontal Stretch: Scale Factor (1/2)

Translation Vector: (3,-10)

I had an attempt in solving the question as follows:

The coefficient of t is 2, because we take the reciprocal of the scale factor

By taking 2 as a common factor:

But it turned out to be wrong, and I have no clue why!

The correct answer is:

Can anyone please tell me what went wrong and how to get this solution?

Thank you!

[Peanut Butter Jelly]

Since you have to do transformations before translations, you need to factor out the two first before adding the translation.

So you have 2t-3

Then you apply the transformation 2(t-1.5-3)=2(t-4.5)

I think...