Question Video: Sketching Curves from their Roots | Nagwa Question Video: Sketching Curves from their Roots | Nagwa

# Question Video: Sketching Curves from their Roots Mathematics

Which of the following is the graph of π(π₯) = (π₯ β 2)Β³? [A] Graph A [B] Graph B [C] Graph C [D] Graph D [E] Graph E.

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### 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 Iβve actually done is Iβve actually drawn a sketch of the graph π¦ equals π₯ cubed or ππ₯ equals π₯ cubed. And as you can see, this actually goes through the origin. To consider how ππ₯ of π₯ minus two all cubed might differ from the ππ₯ equals π₯ cubed graph, weβre actually gonna look at some translations and some rules for these.

The first of which is that ππ₯, 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. Weβre 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 itβs negative π units. And that what it means in practice is that actually weβre 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 weβve got ππ₯ equal to π₯ minus two all cubed. Using our translation rule, therefore we can say that itβs gonna be a shift of negative negative two units in the π₯-direction. And actually, looking at that because it says itβs negative negative two units. What that actually means is weβre actually gonna have a shift of plus two units in the π₯-direction. And what this actually means in practice, is that therefore weβre gonna add two to all of our π₯-coordinates.

Okay, great! Letβs go back to our original graph and see what this would do. So as you can see in the graph thatβs shown in pink, itβll actually shift the whole graph two units to the right because weβve 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 ππ₯ is equal to π₯ minus two all cubed.

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