20 points y=x^3 with the given transformations vertical compression by a factor of 1/7, 8 units to the left, reflection across the x axis

y = (-1/7)(x+8)^3

Start with y = x^3 as given. Multiply the right hand side by the fraction 1/7 so that it is vertically compressed (aka squished) by a factor of 1/7. This means that a point such as (2,8) is now (2,8/7). In other words, it is 7 times shorter in the vertical direction.

Now replace x with (x+8) so that you shift or translate the graph 8 units to the left. What this is effectively doing is moving the xy axis 8 units to the right (whatever x is, add on 8), but if you hold the xy axis still, then it gives the illusion of movement to the left.

The last thing to do is stick a negative out front so that the graph reflects over the x axis.

The order of progression looks like this:

y = x^3 > y = (1/7)*x^3 ---> y = (1/7)*(x+8)^3 ---> y = (-1/7)(x+8)^3