 All right in this video. I'm going to talk about combining transformations combining transformations of linear functions basically what I'm going to be doing is Doing multiple transformations of a linear function So I'm going to be moving it up down left and right and stretching and compressing doing that kind of thing All the videos and all the notes that I've done so far all the examples I've done so far have been just a single transformation and this one kind of goes over just how to do multiple transformations And it's it's relatively simple. It's relatively straightforward What you have to do is you simply these need to take one step at a time just do one transformation at a time and You should be okay with it. Okay, so Reading the directions here let g of x be a horizontal shift left three of f of x equals 3x Followed by a horizontal stretch by a factor of four. Okay, right the new rule right the rule for g of x Okay, now as I said before you just need to basically just take it one step at a time you once one transformation at a time All right, so here's f of x Is 3x and the first thing I want to do is a horizontal shift left three a horizontal shift left three Okay, so what's going to happen is? G of x My new function if I want to move something to the left or to the right I'm either going to add or subtract directly to the x. Okay, so it's going to be x Plus three my zero be plus three or minus three Now if we ever put anything inside parentheses like this It's always going to be opposite of what you think is what I usually say So if I want to move something to the left three, I'm actually going to add three Directly to the x that that will move everything to the left. Okay, and again, it's opposite of what you think That's commonly what I refer to because normally you think okay if I go left that means negative three But not in this case if you ever do that inside the parentheses is always opposite of what you think Okay, now what I'm actually going to do here is I'm actually going to so this is left three Okay, so little arrow for left little arrow for left Okay, left three and now what I'm going to do is I'm actually going to simplify this before I move on so g G of x is equal to three x plus nine Okay, I'm actually going to simplify that a little bit. So actually by moving left three We've actually just a it's basically just a plus nine to my function a little interesting there Anyway now for the second one Okay, so that was the first one just shift left three followed by a horizontal stretch by a factor of four So I'm going to horizontally stretch it by a factor of four now think about it if you horizontally stretch something Horizontal stretching and compressing only affects the slope of your function. It only affects the slope Okay, so it's in our case. It's only going to affect the three here It's not going to affect anything else. Okay, so what I'm going to do now is I'm either going to multiply this times four Or divide by four. That's basically my two choices now think about it We are horizontally stretching if I horizontally stretch a function the slope of the function is actually going to go down Okay, so in that case I need to divide by four. So in this case, I'm going to take my three and I'm going to divide by four Okay, and then this that is going to be a horizontal horizontal Stretch by four and again that only affects the x portion of my Of my function it only affects the slope of my function in this case I had to divide by four. Okay, and that's it That's basically it we just did one at a time the first one that we did was this is left We went to the left three. Okay, and then after that I just just kind of distributed and got this three x plus nine and then a horizontal stretch by a factor of four Which means we divide the slope by four so we get three fourths for a slope three fourths x for a slope and that's it That's basically it just remember when you're doing multiple transformations on a function Just take one step at a time just do one at a time and if you need to do any simplifying like I did here Do that step of simplifying and then apply the new transformation. It just makes things much much easier But anyway, that is how to have just one example of how to do multiple transformations