Which function will have a y-intercept at -1 and an amplitude of 2?

The first and 3rd choices are just sin and cos waves, with amplitude of 1 .
So it has to be the 2nd or 4th choice.

The y-intercept is the point on the graph where x=0.
So if the y-intercept is -1, that just means that  f(0)=-1 .
So let's test the two choices:

                                   f(x) = -2 sin(x) - 1

                                   f(0) = -2 sin(0) - 1
sin(0) = 0  so
                                   f(0) = -2 (0)    - 1 .
That looks like it works.
Just to be sure, let's check the other possible choice.

                                  f(x) = -2 cos(x) - 1

                                 f(0) = -2 cos(0) - 1

cos(0) = 1     so         f(0) = -2 (1)      - 1  =  -3 .  

Beautiful !  The y-intercept of choice-2 is -1,
and the y-intercept of choice-4 is  -3.  The answer is choice-2.