let-fxx-7-and-gxx2-graph-f-and-g-together-with-f-circ-g-and-g-circ-f-3

Question

Let $f(x)=x-7$ and $g(x)=x^{2} .$ Graph $f$ and $g$ together with
$f \circ g$ and $g \circ f$

Nathalie Luna · Accepted Answer

So in this problem we are given two functions as n g x unlike this, and we are asked to graft B composition, both race. So first thing I&#x27;m going to do is I&#x27;m going to grab the original functions. And so here is f of X and read. And here is G effects and blue. So next step is to find out who the compositions are. So 1st 1 is at a key. So this is the same the same and where its argument iss I&#x27;m going to write JFX No next step is and going to like in the definition for chief ex that isthe X squared and no going to use the definition. And that is X minus seven. So instead of X re right here, X squared minus step. So this is going to be this first function the formula for this Rhys function. Now, for the next one, I&#x27;m going to do something very similar. We have gs the outside function and we have f of X as the inside function. So first we write the definition for that isthe X minus seven and next we used definition of G that&#x27;s X squared. So instead of X. We are going to write this new argument that is X minus seven. So this should put enough formula. We could also write this out on DH closet. Plan out. Right, So this would be X squared miners two times seven. It&#x27;s 14 x plus seven squared. That&#x27;s 49. So then this will be the definition for years. Yeah, it&#x27;s in Ross Step two DUIs graphics. We can just punch in these formulas to grow a calculator program. And and here&#x27;s all forthem the red and blue we already talked about. So this purple one is G compulsive f and then the green one is hey!

Ankit Gupta · Answer

you have given and fix equals. Four days. Two x on G f X equals seven days to eggs and reported on the 84 calculator. So we entered the function four days, two x as Y one on seven trays to eggs as I do top on the graph. Pardon and this is what the craft looks like for these two functions.

Lu He · Answer

this question. We need to draw F s first. So half asked. Ego door. Ah, Cube off ass. Who s cube toe? Have a speak o toe as cube. Yeah, and then she as echoed toe ask minus seven Coop, Uh, in minus seven inside the cube. Mario, it means the whole Graf I mean, the f s moved toe life or set, move to write. Buy seven units. So we need if I want in tow. 345 says seven. Okay, so now I use the letter. 3%. Yes, that yesterday days. Okay, thesis drew us. E kowtow s minus seven. Coop, Andi Weaken described us by you by graft. Off of off by saying that off, G, uh, is, uh, transformation off? Oh, uh, s by movie Fast, too. Ah, Roy for seven unit And these

Karly Williams · Answer

Okay, so we need to do is we need to use y equals f of x l plus graph this new equation g of X. So we have to f of X. Well, this is gonna tell us, uh, if we are going to stretch or shrink the graph, if it&#x27;s less than one, but bigger than zero, that it&#x27;s gonna shrink. But if it&#x27;s bigger than one, it&#x27;s gonna stretch. So what this is gonna do is we&#x27;re gonna take our original points, and we&#x27;re gonna apply the y coordinate by our factor. So two times two is four and that goes with both of these. So our new points are going to be negative, too. Four and 247 Take my blue and cloth those now. So since because this is a line it doesn&#x27;t really stretch per se, it just moves it around. However, getting familiar with this procedure can help with other types of equations. But the blue equation from the blue line is our new equation. And the red Green line is our old equation.

Karly Williams · Answer

Okay, so we need to use why Equals of Vex To help graph his equations. We have two times f of X, and that means we&#x27;re going toe have a vertical stretch or shrinkage. But because this is bigger than one, it&#x27;s going to be a vertical stretch. So what we&#x27;re gonna do is around multiply ffx by to so all right, someone split like two. So each of our points it&#x27;s going to be multiplied by two. So are why are why coordinates? Because F of X is equal to y. So that gives us negative four. Actually, let me do this in green. Negative for Tom&#x27;s negative for comma zero, because two times zero is zero than negative. Two times negative four because negative two times two is negative. Four 00 is going to say the same. We have to come before and then four Com zero. So it looks like all of the X intercept stay the same. So we have negative 24 zero and then 24 But in this so we can definitely tell that this has stretched instead of compressed or anything but all of the ones with zero, they&#x27;re going to stay where they&#x27;re at because anything comes. There. It was zero. So green represents our new graph, and Black represents our

Karly Williams · Answer

Okay, So what we&#x27;re gonna dio is we&#x27;re going to use y equals f of X l plus graph this separation. Now we have G of X equals f of two X. So what this, too tells us is that this represents Well, this went to change the horizontal stretch or shrink of this graph. So if it&#x27;s above one that tells us it&#x27;s going to shrink the graph, So what we need to do is I&#x27;m gonna rewrite our coordinates for our original graph now frantic x of both of these and then divide them by kid. So negative to Dodoma two gives us thinking of one and to devote about to Gibson&#x27;s once So a new coordinates are going to be negative. 12 and 12 So I&#x27;m gonna do this in blue. So we have negative one to em in one, too. So our original lime equation is it a grand and road one And then blue is our new equation.

Problem 82 Medium Difficulty

Let $f(x)=x-7$ and $g(x)=x^{2} .$ Graph $f$ and $g$ together with
$f \circ g$ and $g \circ f$

Answer

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Grace H.

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Precalculus Review - Intro

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George B. Thomas Jr.Thomas Calculus

Grace H.

Catherine R.

Anna Marie V.

Caleb E.

George B. Thomas Jr.

Thomas Calculus