Let's see if we can solve this problem. So in this problem, we have a function H of X which is a transformation of the original function F of X is equal to X cubed. We're told in this transformation, the function is reflected over the X axis and then shifted down to units. We're asked to write an equation for H of X and then sketch a graph of the function H of X. So let's begin. Now, first off, we should recognize what type of transformations are happening here. And in this first case, I see that we have a reflection over the X axis recall from previous videos that we, when we reflect over the X axis, our function F of X becomes negative F of X. This is something we learned in the video on reflections. Now we can also see here we have a shift down to units. And since we're only shifted down, this means we're only being vertically shifted. When this happens, our original function F of X becomes F of X plus K where K represents the vertical shift. So these are the two situations we need to watch out for in this problem. Now we'll start things off by taking a look at this function here, which is F of X is equal to X cubed. And what I need to do first is take a look at the first transformation that happens, we see that we're reflected over the X axis. And when this happens, your function becomes negative. So that means X cubed is going to become negative X cubed. This is the first thing that we have where we reflect over the X axis. Now the next thing that happens is the shift down two units. So since we're shifting down two units, this K represents the vertical shift. And since we're shifted down, that means K is going to be negative two for the downward shift. So if we add K to this equation that we have here, our transformation is going to become negative X cubed and then we're going to have minus two because it's a negative two that we plug in for K. So this right here is going to be our transform function H of X. And this is what the new equation is going to look like. So this is how you can figure out what the equation is for H of X. And that's part a of this problem. But we're also asked to sketch a graph of H of X as well and to do this, well, let's just once again, look at the transformations we have, this is the original function right here. And first off, we have a reflection over the x axis, we call that when reflecting over the x axis, you can imagine folding your graph over the X axis, increasing it like a piece of paper. So this portion of the function is going to go kind of down like this and then or more like that and then this portion of the function is going going to fold up kind of like this. So this is what the function will look like when we reflect over the X axis. But we're not quite done yet because notice that we've also been shifted down to units. So this graph is not going to be centered at the origin. It's actually going to be centered down 12 units right here at negative two. So our final graph is going to look like this for the transform function. So this is our transformation H of X as a graph and then this is the corresponding equation. So that is how you can deal with multiple transformations on a single function. Hope you found this helpful.