yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Determining the effects on f(x) = x when replaced by af(x) or f(bx) | Khan Academy


2m read
·Nov 10, 2024

We're told here is a graph of a segment of f of x is equal to x, and so they've graphed that segment right over here. Then they tell us that g of x is equal to -2 times f of x, and they want us to graph g. So think about how you would approach that now. Let's work on this together.

So g of x, whatever x is, I would evaluate f of x, and then I would multiply that by -2. So let's pick, say, when we are at x = 3. f of 3, it looks like that is 3. In fact, we know that's 3 because f of x is equal to x. So f of 3 is 3, but if we want to figure out g of 3, that's going to be f of 3 * -2, which is 3 * -2, which is -6. So f of 3 is -6.

Now let's think about when x is equal to -5. We see that f of 5 is 5, which makes sense. But if we were to take g of 5, that's going to be -2 * f of 5, so it's going to be -2 * 5, which is -10. So it would get us down here.

So really, what you see happening when we multiply f of x by -2, well, if we multiply it by two, we would just be scaling everything up by a factor of two, but then that negative flips it over the x-axis to get what we see right over here.

Let's do another example, but it's going to be a little different. Here, instead of multiplying times our f of x, we're multiplying the x by a number. Here’s a graph of the segment f of x is equal to x; we see that again. Now they've defined h of x as being equal to f of (1/3)x.

So let's graph h. One way to think about it is I know what f of 2 is; f of 2 is equal to 2. Now for h, I could actually input 6 in here. I could figure out what h of 6 is. How do I know what that is? How do I know I can do that? Because h of 6 is going to be f of (1/3) * 6. Another way of saying it, h of 6 is going to be the same thing as f of 2.

So h of 6 is the same thing as f of 2, which is 2. Then we could do that on the negative side. For example, we know that f is defined at -3; f of -3 is -3. Now, if we were to go three times that value and we would say what is h of 9? h of 9, we could go over here. h of 9 is equal to f of (1/3) * 9, or it's going to be the same thing as f of -3. f of -3 is -3, so h of 9 is -3.

So notice now we are scaling; we're making it wider when we multiplied inside of our function. As we multiply x times a fraction, if we multiplied this times a value greater than one, then we would be squeezing it in the horizontal direction.

More Articles

View All
The Multiverse
So we have to come to a deeper understanding of how to explain what is going on in this double state experiment. Because if we fire either a photon or an electron at that double-slit apparatus, and we put a detector at either of those slits, then we will …
MAKE Harry & Hermione KISS .. and other fun free games :)
6 days ago, Little Big Planet 4556 asked for more online scary flash games. So because Vsauce delivers, I’m going to do that right now, along with some funny and just straight up creative games. They’re all free, and they’re all online, and links to them …
Snakes of South America | Primal Survivor
Huh, I thought this was one of the most dangerous snakes in Panama, the fer-de-lance, but this is not. This is a look-alike; this is a cat-eyed snake. But see those markings and see that spearhead-like shape on its head? That makes it look like a fer-de-l…
Khan Academy Live! In Khanversation with Barbara Oakley
So Sal here at Khan Academy worldwide headquarters, and I’m excited to be here with Barbara Oakley, who’s an expert on learning and learning how to learn. So Barbara, let me just start with a question that I’m sure many of Khan Academy users or young peop…
Daily Homeroom with Sal: Monday, April 6
Hello, welcome! This Monday’s a daily homeroom for those of you all who are new here. What this is, something we’re trying to do to keep us all connected as we have the school closures going on throughout the world. Many of y’all know Khan Academy. We’re …
The Lightest Solid on Earth (You won’t believe this exists)
The aerogel shatters into thousands of pieces and turns to dust. But what’s surprising is that if I take those aerogel dusts and apply it to any surface, like my body, it becomes 100% hydrophobic. It makes me completely waterproof. On top of that, this du…