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Graphing cxponential (unctionand it5 @symptotc: Il albl"Graph the exponantial huncton;fk)==Piol Ive points tno graph ol Ihe function , and also Gtam Ine asympl...

Question

Graphing cxponential (unctionand it5 @symptotc: Il albl"Graph the exponantial huncton;fk)==Piol Ive points tno graph ol Ihe function , and also Gtam Ine asymplolo Thon click on the graph-&-lunction Bulton:=plana "sChGckMercBeeksAr

Graphing cxponential (unctionand it5 @symptotc: Il albl" Graph the exponantial huncton; fk)== Piol Ive points tno graph ol Ihe function , and also Gtam Ine asymplolo Thon click on the graph-&-lunction Bulton: =plana "s ChGck MercBeeksAr



Answers

Make a complete graph of the following functions. If an interval is not specified, graph the function on its domain. Use analytical methods and a graphing utility together in a complementary way. $f(x)=3 x^{4}-44 x^{3}+60 x^{2}$ (Hint: Two different graphing windows may be needed.)

Alrighty. So for this problem we have Y equals E to the two X power plus one. So Y equals E to the X powers are original parent function. And so because of that too it's going to be a horizontal shrink. And because of that plus one of the end work's gonna be expecting it to shift everything up one. So we're gonna go to discos dot com to verify our graph and then be able to sketch some ordered pairs and to sketch your graph. So you're gonna go to dismiss that conflict graphing calculator and you'll simply be able to type in the equation as you see it. So y equals e shift six gets us to the exponent area two X. And then plus one. So everything shifted from 01-0 two. So that's one of our points notice that everything went up one and then because of this too that's called a horizontal shrink. And to get some ordered pairs keep in mind is a irrational number. So you're gonna get a lot of decimals, so just bear with that and just do your best, we're going to convert that table Um so that we can have some ordered pair, so we've got negative to a little over the one uh negative one, about 1.1 0-1 is about 8.4 and that's about as far as you're gonna want to be able to go because unfortunately once you hit too, Um it goes all the way up to 55.6%, so it's definitely going to be approaching one here on this side going up and then just going to keep going exponentially more and more and more once once it hits two and beyond. So that should be enough ordered pairs to be able to get a good sketch of the

In discussion of function why is given as it is to depart tours and plus one. We need to plot the graph of this function and then check the graph by using graphing calculator. We also need to describe how we cannot pay the graph of this function using basic exponential functions. So first of all we will substitute the values of X and find out the values of wife in order to plot the graph. We will prepare a table of these values. So here is a table. We will now substitute the values of X and find out the values of Y. First of all, we will substitute X as -4. Yeah, we got right as one and by substituting X as minus three, you will get by again very close to one. By substituting Acts as -2. We will get X as 1.02 and by substituting x s minus right, you will get at right as 1.1 full and by substituting X as zero we will get right as two. And by substituting one, relax you'll get why as 8.29 approx. We can substitute higher release of X greater than mine. But it will result in the value of why much better. Which cannot be plotted on the same draft. So we will talk these points only. And by joining these points using a smooth cow, we will get the graph of this function. So we plotted these points on the graph this is minus four, comma one, this is minus three, comma one, this is minus two, comma 1.2 This is minus one. Comma one point went through. He says, you know, comma two And this is 1:08.39. By joining these points using a smart card. We got the graph of this function boy. We can also check this graph by using a graphing calculator. So now we will describe how we can get the graph of this function. Using basic exponential function. We will consider here S to the power X as the basic exponential function. So as we see the function Y. Is leadership part two X plus. Right? So we write write it called you initiative, eloped two X plus one. And now comparing to the basic exponential function which is G. F. X. Yeah the rest of the power X. So we can see the changes here. X is modified way too and then one is added outside the argument. So for this to multiply by X we will shape the graph horizontally to have. So first transformation will be shrink the growth to have horizontally. At least that among expertise. And second transformation will be for this plus one. It shows that the graph will be shifted up by one unit. So second solution will be to shift the girl. Oh right. Running it so this is the matter by we can obtain the graph of function F of X by using the graph of basic explanation function, which is the rest of the power. X. I hope all of you got discussion. Thank you.

In this question, we have to graft the function. Why equals a to the power X minus two? Using the graphing calculator, we get the graph as like this.

Were given a graph of two functions F n G, and were asked to graph these some of these functions each so the functions are featured in exercise three of this section. Now, for these functions, we see that these air piece wise linear functions. Therefore, in order to graph our function, H, we're going to calculate the values of h of X at X equals one to three and zero and then we'll interpret late. There is in this interpolation is possible is precisely because FN gear both piece wise linear therefore h of x is piece wise, linear and is the interpolation of these points. So to do this, we'll make a table. So for this table, the first row will be values of X second ffx, third g of X and the fourth H, which is F plus g of X now for X. As I pointed out before, we want to calculate the values at each of the end points of the piece wise linear segments of F. G. So we see that F and G have peaceful eyes, linear segments with end points at 012 and three. So we have f of zero we see from our graph this is to and G of zero we see from the graph is a negative one and therefore H each of zero is F plus g of zero, which is F zero plus g of zero is two plus negative one or one. Likewise, we see from the graph that f of one is three g of 10 Therefore, h of one is one on the graph. We see the f of two is one G F two is about one half. Therefore h of two is about three halves and finally f of three is too g of 30 and each of three is going to be two plus zero, which is to So we have these four points for H. So now let's get a graph of h mhm. We see that X ranges from 0 to 3 and y from 1 to 2. Saw graph on the X axis from 0 to 3 on the Y axis from 0 to 3 as well. So you have a job. Zero. This is one dress in green. We have a judge of one is one also Each of two is three halves it's about here in each of three is two, which is here. And as I said before, I'm sorry, Miss. Take here f of one should be three, not one. So if that's three than h of one is also three, okay, And then we have point here at 13 for age. And then, as I pointed out before, because both f n g or piece wise linear, we have that DeGraff H is also going to be peace wise veneer. And so we simply interpret late. And this is the graph for function h.


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