Use the graph of

Question

Use the graph of $f$ in the figure to plot the following functions.

$y=f\left(x-2\right)$

Accepted Answer

Hello there today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Given the graph of the function G of X plot the graph Y equals G of X plus three. Awesome. So it appears for this particular problem we're trying to take our original function which is G of X and we're trying to use it to help us plot our new graph using a transformation for Y equals G of X plus three. Awesome. So looking at our graph, it appears we have a lightning bolt shape for Y equals G FX and we have a point at 22 as we could see and I will put a red dot our graph itself is in red and we have a point at 22 and then we have another point at negative 24. And what we're trying to do is is we're trying to use transformations to take our original graph, which is Y equals G of X and we're trying to transform it to Y equals G of X plus three. Awesome. So we need to note that and let's call, it's gonna call our new graph to be, let's do blue to represent our new graph. So we're trying to say that the graph for Y equals G of X plus three because we have a plus three here, which I'll underline in red, this plus three. So it's X plus three, this plus three indicates that we're gonna have to shift our graph three units to the left. If this was X minus three, we would be shifting our graph three units to the right. But since it's plus three, we're adding three to X, that means we're moving our graph three units to the left. So with that said, using our blue marker here, we're gonna go, let's start with our 22 point. We're gonna be moving three points. So 12 and three, we're gonna be moving it three points. So we're gonna be taking it. So let's say that halfway point is one. So 12 and three. So that would mean that our new point would be here for our 22 would be shifted three units to the left. So now it's gonna be at 12 and then our next point which was at negative two or now we're gonna be moving it three, we're gonna be moving at three units to the left. So 12 and three, it will now be at 54, negative 54 to be precise. So when we take this information and let's plug this into our graphing calculator, so we can get an accurate visualization of what this graph would look like. So when we do that, I've gone ahead and plugged it into my graphing calculator or you could use whatever graphing software that's easy for you to use that you understand, to use. So when you plug in your expression for Y equals G of X plus three, you will see that our new graph, which as we said discussed, our new points will be at negative 12 and at negative 54. So as you could see our graph stays exactly the same as Y equals G FX. But all it is is that our graph has been shifted three units to the left. So everything stays the same, but the position changes because it's been shoved or pushed three units to the left and that's it you've solved for this problem. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

Use the graph of $f$ in the figure to plot the following functions.
<IMAGE>
$y=f\left(x-2\right)$

Watch next

Use the graph of ﻿fff﻿ in the figure to plot the following functions.<IMAGE>﻿y=f(x−2)y=f\left(x-2\right)y=f(x−2)﻿

Watch next

Use the graph of $f$ in the figure to plot the following functions.
<IMAGE>
$y=f\left(x-2\right)$