The graph of ƒ is shown in the figure. Graph the following fun...

Question

The graph of ƒ is shown in the figure. Graph the following functions.

a. $f with hook open paren x plus 1 close paren$

Accepted Answer

Below 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 function H of X sketch the graph of the function H of X plus three. Awesome. So it appears for this particular problem, we're gonna be taking our original function which is H of X, which is plotted right now on the graph that's provided to us by the prom itself. And we're gonna be applying transformations to this original graph of H of X to receive the following graph of the function H of X plus three. So now that we know that our function now, which we're trying to ultimately, and let's write this in red. We're trying to figure out a graph for H of X equals. So we're trying to figure out our function, not I said H of X. So we're trying to say H of X plus three, that's our new graph that we're trying to plot in red. So essentially, it's important to note that we're gonna be applying transformations because what's changed instead of it being just X, we're adding 32 X and because we're adding three to X, that means we're gonna be shifting our graph three units to the left. So that means looking at our graph here. So let's look at our plot here. So right now, let's just say for simplicity, like simplicity's sake, even though it's not quite at one, we'll just say that it's at one negative 30 for our first plot. And then for our second plot, it's at negative one about negative one and negative 30. And I drew little red dots to indicate the different plots. So this is at roughly one comma negative 30 for one dot And the other dot or plot I should say is at negative one negative 30. Roughly it's not exact, just roughly just looking at the graph itself. So essentially what we're gonna be doing is we're gonna be taking these points and we're gonna be shifting it three units to the left. So the original graph is just gonna be moving three units to the left. Nothing else is gonna change other than its location. So with that in mind, we're gonna be going 12 and three. So we're gonna be moving three to the left and then our other plot 12 and three. So as you can see it shifted off to the side, so using my graphing calculator or whatever graphing software works well for you as you could see, I plotted in our, I plotted it in my graphing software and then I screenshotted it to share with you. And as you could see exact same graph as the original function, but it's been shifted three units to the left. And as you could see where we plotted it together, we did really well for a little rough estimate here in red because as you could see our new plots now, as we could see are gonna be for our two little plots. So it's gonna be at just slightly be slightly past the vertical axe to the left, just a, just a hair. And then we could see it's about, let's just say negative eight. So it's at negative eight, negative 30 for our one point. So we can write that down. So negative eight, negative 30 for one point. And then we could say that like I said, it was about one before we could just say it's about hm like maybe a little bit less for other point. We could just say that maybe it's like at negative 0.9 to negative 30 more or less. This is just an estimate just like looking at the graph is it's a little bit past, you know, it's past zero but not quite one. It doesn't look like it's not quite one. So like 0.9 negative 0.9 just estimate. So basically, all we're doing is we're taking our original function and we're just shifting it once again, three units to the left and that's it you've officially solved for this problem. Hooray. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

The graph of ƒ is shown in the figure. Graph the following functions. <IMAGE>
a. $f with hook open paren x plus 1 close paren$

Key Concepts

Function Transformation

Horizontal Shift

Graphing Functions

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