### Video Transcript

Which of the following is the graph of π π₯ equals π₯ minus two all cubed?

To start off solving this problem, what Iβve actually done is Iβve actually drawn a sketch of the graph π¦ equals π₯ cubed or ππ₯ equals π₯ cubed. And as you can see, this actually goes through the origin. To consider how ππ₯ of π₯ minus two all cubed might differ from the ππ₯ equals π₯ cubed graph, weβre actually gonna look at some translations and some rules for these.

The first of which is that ππ₯, in parentheses, plus π, that will give us a shift of π units in the π¦-direction. What does this mean in practice? Well, it actually means that all of our π¦-coordinates would actually add π to each of those to actually give us what our shift would be.

Okay. Weβre gonna have a look at another translation. And our second translation rule tells us that π of π₯ plus π, this time the plus π is in the parentheses. And this means a shift of negative π units in the π₯-direction. Remember you need to pay particular attention to the fact that itβs negative π units. And that what it means in practice is that actually weβre gonna subtract π from each of the π₯-coordinates in order to actually show how our graph has shifted.

Okay. So if we look back at our function, so weβve got ππ₯ equal to π₯ minus two all cubed. Using our translation rule, therefore we can say that itβs gonna be a shift of negative negative two units in the π₯-direction. And actually, looking at that because it says itβs negative negative two units. What that actually means is weβre actually gonna have a shift of plus two units in the π₯-direction. And what this actually means in practice, is that therefore weβre gonna add two to all of our π₯-coordinates.

Okay, great! Letβs go back to our original graph and see what this would do. So as you can see in the graph thatβs shown in pink, itβll actually shift the whole graph two units to the right because weβve actually added two to every π₯-coordinate. And therefore, fantastic! We can actually see which is the correct answer. We look back at π. So π is our correct answer because we can actually see that the intercept there would be at two.

So π is the correct graph of ππ₯ is equal to π₯ minus two all cubed.