5

Sketch a graph of a function f(x) where:f (x) < 0 forx < 1 f (x) > 0 for x > 1and f (x) > 0 for allxSketch a graph of a function g(x) where:9 (x) >...

Question

Sketch a graph of a function f(x) where:f (x) < 0 forx < 1 f (x) > 0 for x > 1and f (x) > 0 for allxSketch a graph of a function g(x) where:9 (x) > 0 forx < 29 (x) < 0 for x > 2and g (x) < 0 for allxSketch a graph of a function h(x) where: h"(x) < 0 forx < 3 h"(x) > 0 forx > 3 and 'h'(x) > 0 for allx

Sketch a graph of a function f(x) where: f (x) < 0 forx < 1 f (x) > 0 for x > 1 and f (x) > 0 for allx Sketch a graph of a function g(x) where: 9 (x) > 0 forx < 2 9 (x) < 0 for x > 2 and g (x) < 0 for allx Sketch a graph of a function h(x) where: h"(x) < 0 forx < 3 h"(x) > 0 forx > 3 and 'h'(x) > 0 for allx



Answers

Sketch the graph of the piecewise defined function.
$f(x)=\left\{\begin{array}{ll}{-x} & {\text { if } x \leq 0} \\ {9-x^{2}} & {\text { if } 0< x \leq 3} \\ {x-3} & {\text { if } x>3}\end{array}\right.$

Um, this is one off the graph. A sketch for this problem. Um, first, we noticed that this f on the function f is an old function. Let me in this work we only folk song zero to infinitely and no enough. The other part of the Red Line parties that were this symmetry about X equals zero. Okay, So from the information we know from 0 to 2, um, from X from 0 to 2, um, f is increasing and the front foot infinity if it's decreasing and we already know, uh, X equal to three, there's an inflection points. This is the inflection point on its right. The curve is coming down and on council left the cave The coffee's can kept on and on to Writer Kofi's concrete. Also, there's the horizontal seem totally xy costa. What here since like this, Why coast once or so westway finish the positive parts. We just do the symmetric Ah, curve for the negative part and that's there. So be careful about this. If we don't asymmetry curve, another sympathetic um horizontal syntactic will be X equals two minds. Why? It cost to minus one

For the following problem, we're going to sketch the graphs of the following functions. That's going to be f of X equals three X. That's when actors between zero and 1. And then we're going to have um 9/2 -3/2. That's going to be when X is greater than one. We end up getting this right here as our function and then we want to consider Um one plus X one, X is less than or equal to three and then um four When X is greater than three. So you see those are two different cases of piecewise functions, but we can combine two different graphs in multiple ways, as long as we restrict their domains. And by doing so, we have two completely new graphs for these two problems.

Given function is FX equals minus X. If the value of X is less than it goes to zero on FX equals nine minus X square in the value of X is between zero. Entry were three is included on affects equals X minus three If X is greater than three. No firstly deplored the graph of dysfunction. Guilty. If X is less than it goes to zero, then our function FX is then I function effects equals two minus X. Now, the graph of this function is similar to the graph off equation by equals two minus eggs and we will now to some values off X, for which we will try to compute the corresponding value of ethics. So, firstly, we need to choose the values off Exeter less than equals 20 So values of x zero minus one and minus two. So for these values off X r value off FX is 01 and two lording these points on a graph we get, This is the point zero comma zero and since this point is included in this part off our graph, so we will make a solid or tail to represent that this is included. This point is minus one comma one. This point is minus two Komodo. So we applauded these points. Now, connecting all these points, we get the graph, we get the part off our graph, which is lying left to the point X equals 20 now. Secondly, if we take the value off expert with zero and three were three is included, then our function F X is nine minus X squared, which is on the graph of function. F X equals to nine minus. X squared coincides with a graph off equation by equals through nine minus X squared. Now we will try to upload the graph of dysfunction by plotting the points, do some values off X and then find the corresponding values off ethics. The leaves off extra built between zero entry where three can be included. So I don't think the values 12 and three corresponding values off FX are it five AM zero. No bloating these points. This is a point. Good. My point is zero coma nine and saying this point is not included, Sybil maker or panned out here. To represent that this point is not included. But at this 0.0 common in as if we put the value of excess zero hill. Our value of effects becomes nine. So this point is one go my aid tokuma five. And lastly, this point is three coma zero. Now connecting these points, we get another part offer graph which is a parabola Now, lastly, if we take the value off X greater than three, then FX is X minus three and the graph of function effects equals two X minus three coincides with the graph of figuration. X equation y equals X minus three. Now we will take some values of X and find correspondingly off FX. It is X minus tree. Now there's some values off X that we, too should be greater than three. Therefore, X must be 456 and you can take another values also So for X equals one FX is so for X equals for the value of FX is one for X equals five. The value of FX is to and for X equals six. The value off FX is three floating these points here we get these points which are for coma one five Coomer two and six coma three now connecting all these points, I get the remaining part off my graph, which is like this. And since X equals 23 is not included. Therefore, I will make an open door here to represent that This point is not included in this point part of the ground. While this point was included in this part of the gravity is a parabola. So I've got the equation. I have floated the graph off this equation or dysfunction, which was peace wide piece wise, defined function given to us.

In this problem. Um, we want to scrap. We want a sketch. A graph of a function where f zero equals zero f prime of zero equals zero f Prime of X is greater than zero for all X, less than zero or X greater than zero. So let's go ahead and draw axes Your wine. I'm sorry, your ex and your wife and we know So we know the point zero comma zero because we have, um we know that f of 00 And we also know that our slope is gonna be zero at that point. So there's, like, a potential tangent line. Well, actually, it would be a change that line. Um, so then what else do we know? So we know that, um, when X is less than zero, we have positive slope, so it's gonna be like going up, and we know that when X is greater than zero slope is also greater than zero. So that means after this point, the slopes gonna be going up. And if the slope, if the if the function is increasing after a 00 then it's gonna be above the X axis. And if it's increasing before 00 Then we know it's below the X axis because it has to come up to meet that 0.0 So from here, you can just pick any function, you know, that satisfies these conditions. So after top my head, like, why equals X cubed? That kind of shape is gonna mimic the behavior that's described in this problem. So we have zero slope in the center and then positive slope on the left and right. Get rid of these rings. We got rid of everything, something like this.


Similar Solved Questions

5 answers
Normal 510K, temperature point is critical Jullloq and 1 pue n8Satroser compound ouredoy Igrariple dia 350k, pointase the Sketch freezing 944K. 12.179
normal 510K, temperature point is critical Jullloq and 1 pue n8Satroser compound ouredoy Igrariple dia 350k, pointase the Sketch freezing 944K. 12. 179...
5 answers
The Find the function s(t) 2 879 velodty function vt) describes 32t + motion ontne particle particle u( Jt alonq UmeIdentify the 1 intervalls) on which the particle Ioyingthe time(s) whichtme intervalls) which tne panticieparucla clange'1posiuve durection (Entam1comme 11 Intenya Inoteteie1 1 1 niaenet
The Find the function s(t) 2 879 velodty function vt) describes 32t + motion ontne particle particle u( Jt alonq Ume Identify the 1 intervalls) on which the particle Ioying the time(s) which tme intervalls) which tne panticie parucla clange' 1 posiuve durection (Entam 1 comme 1 1 Intenya Inote...
5 answers
[on1 PointsFind the total dilierenbul6x9 8541816Nccd Help?ual manuafSubak Answer[O1 Points]CetAIJetuuAttiLARCALC9 13.4002Lolal ahdautlilHeed Help?[-71 Points]DETAMILARCALCE 13,4,004.Andthatoula Acrental_Need Help?0-/1 Points]DMUL}LARCALC' 13 4C02Fing thetotl Gime s FitNeea Help?
[on1 Points Find the total dilierenbul 6x9 8 541816 Nccd Help? ual manuaf Subak Answer [O1 Points] CetAI JetuuAtti LARCALC9 13.4002 Lolal ahdautlil Heed Help? [-71 Points] DETAMI LARCALCE 13,4,004. Andthatoula Acrental_ Need Help? 0-/1 Points] DMUL} LARCALC' 13 4C02 Fing thetotl Gime s Fit Nee...
5 answers
How can the standard error of estimate be interpreled?The standard prtror oslimato Ihe sulos Ior specilic total square foolage about billion dollars. The standard ofror ostimale of the total square tootago for spocilic numbor of aal0s about billion [ dollars.
How can the standard error of estimate be interpreled? The standard prtror oslimato Ihe sulos Ior specilic total square foolage about billion dollars. The standard ofror ostimale of the total square tootago for spocilic numbor of aal0s about billion [ dollars....
5 answers
Define g R = R byG) if ~ = !/n for some eN_ 9(1) ~{ if _ =0. Prove that g is continuous at 0_
Define g R = R by G) if ~ = !/n for some eN_ 9(1) ~{ if _ =0. Prove that g is continuous at 0_...
5 answers
Histidine has (hree ionizable groups; with pKa values of 2 6.0 and 9 A L.OL solution ofo5M histidine has pH of 2. To this solution. YOu add [.0 Mof NaOH: What is the pH of this final solution?(B)(E) 9,6
Histidine has (hree ionizable groups; with pKa values of 2 6.0 and 9 A L.OL solution ofo5M histidine has pH of 2. To this solution. YOu add [.0 Mof NaOH: What is the pH of this final solution? (B) (E) 9,6...
5 answers
Question 2 (1 point) Which of the following is NOT shared by Bryophytes and Charophytes?sporopollenincell wall containing cellulosephragmoplastphotoautotrophymulticellular diploid structures
Question 2 (1 point) Which of the following is NOT shared by Bryophytes and Charophytes? sporopollenin cell wall containing cellulose phragmoplast photoautotrophy multicellular diploid structures...
5 answers
Table 1.2 pH electrode readings from Part !. Solution Initial pH pH after the addition of HCI pH after the addition of NaOH9.307.7711.457.637.2010.2437.156.717.4946.635.577.1054.732.766.516.982.9512.65
Table 1.2 pH electrode readings from Part !. Solution Initial pH pH after the addition of HCI pH after the addition of NaOH 9.30 7.77 11.45 7.63 7.20 10.24 3 7.15 6.71 7.49 4 6.63 5.57 7.10 5 4.73 2.76 6.51 6.98 2.95 12.65...
5 answers
Individuals marrying into the family are homozygous for the wild-type allele. What is the most likely mode of inheritance for pedigree What is the most likely mode of inheritance for pedigree III578 88888886
individuals marrying into the family are homozygous for the wild-type allele. What is the most likely mode of inheritance for pedigree What is the most likely mode of inheritance for pedigree III 578 88888886...
5 answers
Solve each formula for the specified variable. The use of the formula is indicated in parentheses.$S= rac{a_{1}-a_{1} r^{n}}{1-r}$ for $a_{1}$ (geometric series)
Solve each formula for the specified variable. The use of the formula is indicated in parentheses. $S=\frac{a_{1}-a_{1} r^{n}}{1-r}$ for $a_{1}$ (geometric series)...
5 answers
Write an equation in standard form of each hyperbola described.Center $(2,4) ; a=2, b=3 ;$ transverse axis is horizontal
Write an equation in standard form of each hyperbola described. Center $(2,4) ; a=2, b=3 ;$ transverse axis is horizontal...
5 answers
13 MZ1 Ppines][email protected] 10 2 005Findlan equahlonucfhehehnanoeetouthe GwmeHathheknoLkGrkedpomdicg tahthenghvenimaluelofithe parameter: KhHeoNGemh HMMESIGGUHHu MHHHHTUMlLIeveipenE IIDAaLHBIRREWDUSIMAMERAIcAldemaloiies
13 MZ1 Ppines] ELUNLE @NEnEUSANELHERU ECALCETS 10 2 005 Findlan equahlonucfhehehnanoeetouthe GwmeHathheknoLkGrkedpomdicg tahthenghvenimaluelofithe parameter: KhHeoNGemh HMMESIGGUH Hu MHHHHTU MlL IeveipenE I IDAaLHB IRREWDUSIMAMERA IcAldemaloiies...
5 answers
Below is distribution for number of visits to dentists in one year:Type numhers in the barePart I 2 pointsPart 2: pointsPant 3: 2 pointsFant # DointP(Xex)228 0.43 0.15 0.06 0.08Pant 5: _ 'painspointsCalculate the following probabilities:a. P(X < 2) =b. PCX > 3)P(I< X < 3) =dP(3 < X< 5) =e: P(3 < X <5)
Below is distribution for number of visits to dentists in one year: Type numhers in the bare Part I 2 points Part 2: points Pant 3: 2 points Fant # Doint P(Xex) 228 0.43 0.15 0.06 0.08 Pant 5: _ 'pains points Calculate the following probabilities: a. P(X < 2) = b. PCX > 3) P(I< X < ...
5 answers
Q2 Write the eight steps of krebs cycle in details and show how many ATP/ Coenzymes are produced in each step:
Q2 Write the eight steps of krebs cycle in details and show how many ATP/ Coenzymes are produced in each step:...
5 answers
The point E(-7.-24) lies on the circle whose equation is x +y' 625 , If an angle drawn in standard position and its terminal ray passes through E. what is the value of the sine of this angle?(I) -7724
The point E(-7.-24) lies on the circle whose equation is x +y' 625 , If an angle drawn in standard position and its terminal ray passes through E. what is the value of the sine of this angle? (I) -7 724...
5 answers
Fina the average value of the function f over the interval [0, 12].5 flx) = x+ 1
Fina the average value of the function f over the interval [0, 12]. 5 flx) = x+ 1...

-- 0.023483--