5

Sketch the graph of $f(x)=x^{3}$ and the graph of the function $g .$ Describe the transformation from $f$ to $g .$$$g(x)=(x-2)^{3}-3$$...

Question

Sketch the graph of $f(x)=x^{3}$ and the graph of the function $g .$ Describe the transformation from $f$ to $g .$$$g(x)=(x-2)^{3}-3$$

Sketch the graph of $f(x)=x^{3}$ and the graph of the function $g .$ Describe the transformation from $f$ to $g .$ $$g(x)=(x-2)^{3}-3$$



Answers

describe how the graph of each function is a transformation of the graph of the original function $f.$
$$g(x)=f\left(\frac{1}{3} x\right)$$

Given the function G of X is equal to three times f of negative X. What are the transformations that have happened on F to get to G? Okay, so the first thing we want to look at is the differences between F and G. We see here the differences are this three on the outside of the function and this negative on the inside. Okay, so remember that when a transformation is happening on the inside of that function, it's happening before the function. F performs any of its operations. And when it is outside the function like three, it's happening after the function. F has performed all of its operations. Okay, so let's consider an example. Let's say that f of X is something like X cubed. You can't. So it's going something like this. Okay, let's consider a point on our function s Okay, let's call it the point. A be okay. So we have this point. Let's consider first how the negative on the inside of the function is going toe effect that point so effectively. All we're doing is taking all of our positive X values and making the negative and all of our negative values of making them positive. So if a B is a point on F, then negative A B is going to be a point on f of negative X. Okay, that's gonna pull that point exactly the same distance to the other side of the Y axis. Okay. And the fact that that's the same distance is what tells us that we have a reflection across the Y axis. Okay, so now this is going to be negative. A And then that's going to happen to every single point along the graph. So the transformed functions gonna look something like this. Okay, so that's the negative. Let's look at the three. Okay, so we see because of three is on the outside of the function, it's going to apply to our Why values. So that's that's effectively going to take each individual. Why value for every single ordered pair and multiply it by three. So the new point after this transformation, it's gonna be way up here, and it's going to be negative. A three b. Okay, so what we're doing is we're taken every single point on this green graph, and we're pulling it up. We're gonna stretch it vertically, OK, until each point is three times higher than where it originally waas. Okay, And that's gonna be the same thing on this negative part of the graph. We're gonna stretch it until it is three times further away than where it started. So the graph is gonna look something like this. Okay, so putting it all together, we see that G is a reflection across the Y axis, okay? And a vertical stretch with a factor of three. Okay, so that's how I like to consider transformations that are the effect of multiples on the inside and outside of the function.

Given the G of X is equal to negative of three X What transformations happened on F to get G? Well, the first thing that I want to do is look at the differences between G and F, and we see that those differences are this negative outside and this three inside the parentheses. Okay, so let's remember things that happened inside. The parentheses happen in the X direction and things outside the parentheses happen in the Y direction. So what I want to do is start with the inside. So for a second I'm just going to ignore the negative. Okay, so let's consider a few values. This let's look at G of one that's gonna be equal to f of three. Do you have to? Is going to equal G at six and so on. You can see that if these different X values they're going to have the same why value or in other words, G is going to reach a certain value of why three times earlier than F. Okay, so let's consider an example. Let's say that f looks something like X squared. OK, so we have something look, something like this. Okay, so what's look first at That's a three. So that spot that dot right there is three f of three, right? So that height is going to be the same as G of one, right? So if here's one G is going to have that same height, okay? And that's going to happen along the entire domain of F, every single point is going to effectively get squished inward, right? And that by a factor of three. Okay, so g is gonna look something like this, right? That's the first thing we have. We have a horizontal compression by a factor of three. Okay, so now let's look at that negative. What it's going to do is take every positive y value and make it negative and every negative y value and make it positive. Okay, So if we look at our graph after the first transformation, we're now going to take every point and move it where it is to the other side. Two of the X axis, okay, with same just since it is above, it's not gonna be below. Okay, so that, in effect, is going to be a reflection across the X axis. That's gonna be our 2nd 1 we're gonna have a reflection across the X axis. Okay, So those are the two transformations that have taken place on F to get to G.

The function not given us A X equals x Q Bangi X equals minus X cubed. So to floored us on the calculator for its present by equals button. Then type in the function X cubed, then type in the second function minus X cubed. You have to use this trick that is to put zero in front as the calculator show Eddo. So type it are soon in the video, the craft, and do that. Therefore, we noticed that there is a reflection across X access.

So in this question, I have the graph off if X equal to X cube. So let me name the graph. This is affecting Koldo X Cube. No, I have to draw the graph off DXC Carletto X minus three Whole cube. So explain a three hole killed will be simply the roots off. This DX will be at three com. A zero on the same graph will be Replicator as it is passing through this 0.3 comma zero Onda raising up, running parallel to the and fixed it up. So that's how McGraw Office this is for Vieques.


Similar Solved Questions

5 answers
Convert the following measurement_mol :I0l -dL
Convert the following measurement_ mol : I0l -dL...
5 answers
Find te cxact vali: of ccs(355" )Findco 29 ir ccc8and 8 ic in quadant IV.If sn8=-$ and I < 8 < 5 find cos8Fovc3ec8s 8 co8 + "3118
Find te cxact vali: of ccs(355" ) Findco 29 ir ccc8 and 8 ic in quadant IV. If sn8=-$ and I < 8 < 5 find cos8 Fovc 3ec8 s 8 co8 + "3118...
5 answers
(a) Find the center of mass of a 1D rod (length L) that is positioned along the V-axis and has the linear mass density A(y) = bVy where b is a constant: (b) If the total mass of the rod is M, find b in terms of Mand L
(a) Find the center of mass of a 1D rod (length L) that is positioned along the V-axis and has the linear mass density A(y) = bVy where b is a constant: (b) If the total mass of the rod is M, find b in terms of Mand L...
5 answers
Consider The function: Y(x) = 15 + Se sin (x + Develop script to co-plot Ylx) for Raalun three values . of omega W 9,13 and 15 _ with x-interval 0 < x < 15 in steps of 0.1. Seconas The final plot should have the following attributes: Graph Title: Y(x) = 15 + sin @x + 3 Jx-axis Time (s); v-label y(x); Line type W=9 Solid line; W=13 Dashed Iine and W=15 Dotted Line; Grid On_
Consider The function: Y(x) = 15 + Se sin (x + Develop script to co-plot Ylx) for Raalun three values . of omega W 9,13 and 15 _ with x-interval 0 < x < 15 in steps of 0.1. Seconas The final plot should have the following attributes: Graph Title: Y(x) = 15 + sin @x + 3 Jx-axis Time (s); v-labe...
5 answers
A voltaic cell consists of an Mn/Mn2+ half-cell and a Pb/Pbl+ half-cell. Calculate [Pb?+ ] when [Mn?+] is 1.4 M and E is 0.44 V: cell[Pb?+] p.94 02217Enter your answer in scientific notation.
A voltaic cell consists of an Mn/Mn2+ half-cell and a Pb/Pbl+ half-cell. Calculate [Pb?+ ] when [Mn?+] is 1.4 M and E is 0.44 V: cell [Pb?+] p.94 02217 Enter your answer in scientific notation....
5 answers
Consider the following reaction: Sn(s) Ozlg) SnOz(g) delta H 577.6 kWhich of the graphs correctly diagrams the potential energy during the course of the reaction?
Consider the following reaction: Sn(s) Ozlg) SnOz(g) delta H 577.6 k Which of the graphs correctly diagrams the potential energy during the course of the reaction?...
5 answers
Bank of Nassau is offering CD that E pays 4% compounded continuously: How much interest would 54,000 deposit earn over 12 years? Round your dollar. answer t0 the nearest (f points) Ale) p U+x 1 2 0y 5,553( 10 7.tly ~84 6 3 4joooStrent with an Interest rate 0f 2.596 [0 montns Round the answer t0 points)ncarest YEJ tne How long if the Unterest valuc _ triple Its the neatest
Bank of Nassau is offering CD that E pays 4% compounded continuously: How much interest would 54,000 deposit earn over 12 years? Round your dollar. answer t0 the nearest (f points) Ale) p U+x 1 2 0y 5,553( 10 7.tly ~84 6 3 4jooo Strent with an Interest rate 0f 2.596 [0 montns Round the answer t0 p...
5 answers
[-14 Points]DETAILSLARCALCET7 5.4.046,EP,(eDint'ullowing ILnO -~Svr. [4 9] continudut the dosrd (reryal 0,6] = [4 91Gvnluste {ne Integralaqualonnles Ach(oDtinruneLeuHeat 'Unareted lal)"m d
[-14 Points] DETAILS LARCALCET7 5.4.046,EP, (eDint 'ullowing ILnO - ~Svr. [4 9] continudut the dosrd (reryal 0,6] = [4 91 Gvnluste {ne Integral aqualon nles Ach(o DtinruneLeuHeat 'Unareted lal) "m d...
2 answers
What iIs the volume of a cylindrical disk? Explaln how to use slicing to find the volume of a solid of revolution: Why might You need to use the slicing of washers versus disks? Please respond t0 at least one (1) of your classmate'$ posting.
What iIs the volume of a cylindrical disk? Explaln how to use slicing to find the volume of a solid of revolution: Why might You need to use the slicing of washers versus disks? Please respond t0 at least one (1) of your classmate'$ posting....
1 answers
Let $D$ be the region bounded below by the cone $z=\sqrt{x^{2}+y^{2}}$ and above by the plane $z=1 .$ Set up the triple integrals in spherical coordinates that give the volume of $D$ using the following orders of integration. a. $d \rho d \phi d \theta$ b. $d \phi d \rho d \theta$
Let $D$ be the region bounded below by the cone $z=\sqrt{x^{2}+y^{2}}$ and above by the plane $z=1 .$ Set up the triple integrals in spherical coordinates that give the volume of $D$ using the following orders of integration. a. $d \rho d \phi d \theta$ b. $d \phi d \rho d \theta$...
5 answers
Ho_Hc _scoiic-OHHc 8-04Use the above catalytic cycle above. What are the names of step B and E, respectively?Select one: 1. B: OA and E: hydrolysis2. B: RE and E :RE3. B: alkyl migration and E: hydrolysis4.B: CO insertion and E: acid base reaction5. B: hydrolysis and E: acid base reaction
Ho_ Hc _ sco iic-OH Hc 8-04 Use the above catalytic cycle above. What are the names of step B and E, respectively? Select one: 1. B: OA and E: hydrolysis 2. B: RE and E :RE 3. B: alkyl migration and E: hydrolysis 4.B: CO insertion and E: acid base reaction 5. B: hydrolysis and E: acid base reaction...
5 answers
47 otagonul base br R}61lieta T3-[-13 sdx-| = Balnaetn Re, Ian the nwntan GIioieal Ind edun anoonont AamnettheHenett Tien > nun nucdenutlvI4 unducetounhtot by=uach uanchOdtonnHnehelonnnhnAupeloried next?Emalbtour ntworVnbnahcnCmtcntnanutML 0.4ochorolal buila Iot R) >WernmnentmErntul titovockntSinca ooth"0 FCLd Ennanncnmenalon %neu*Frnronq0+DD, (Uta Iejor Irnctoa lor nnanlTbrnFalmonCick e ealoct your answerlg}
47 otagonul base br R} 61lieta T3-[-13 sdx-| = Balnaetn Re, Ian the nwntan GIioieal Ind edun anoonont AamnettheHenett Tien > nun nucdenut lvI4 unducetounhtot by= uach u anch Odtonn HnehelonnnhnAu peloried next? Emalbtour ntwor Vn bnahcnCmtcntnanutML 0.4 ochorolal buila Iot R) > Wernmnentm Ernt...
5 answers
Comment on tneir of T cells and Name two types RECo.5] origin in one sentence hallmark of factor that is Name the transcription cells. One word: [0.5] TREG in 5 sentences or how T cells inhibit APCs Explain REG less. [2] cells inhibit other effector T cells Explain how TREG in 5 sentences or less_ [2]
comment on tneir of T cells and Name two types RECo.5] origin in one sentence hallmark of factor that is Name the transcription cells. One word: [0.5] TREG in 5 sentences or how T cells inhibit APCs Explain REG less. [2] cells inhibit other effector T cells Explain how TREG in 5 sentences or less_ [...
5 answers
Task4 Eau-lnneAl check the solution(s) ~unation HIllFirl Identify the doqain; second; solve4 UasiVr+T+1= V Tk - 1) (7+/3X +33x + | X1 2 ~3 K--1J N-S+z=5)" MX-s ~ 22S 9s-v ) ? (N-s X-$ = "s - x) 2 6a5 -x 2 K-s2018, Taylor Revised spring
Task4 Eau-lnne Al check the solution(s) ~unation HIll Firl Identify the doqain; second; solve 4 Uasi Vr+T+1= V Tk - 1) (7+/ 3X + 3 3x + | X1 2 ~3 K--1J N-S+z=5)" MX-s ~ 22S 9s-v ) ? (N-s X-$ = "s - x) 2 6a5 -x 2 K-s 2018, Taylor Revised spring...
5 answers
BMcc atudenta wore abk0d how many houte pet nohl they llocp Tha rertll ol iu buntu cno Holt C FlaquurcyFind; and Etandurd covial on sandard devlation ol Ihe moantIno numduthours 01 eloop (or this sumple Whal perceni tho dala Iias WuninDraw relalive frequency histogram Andan oqive: Doscribe Ihe shape approximaic Ie medlanIhe hislogram shoanok Ua8 Ine OQWvoIhis survoy? What type dala Wos Dalhered? What 5 the sample, the populatlon: statistic , and parameler
BMcc atudenta wore abk0d how many houte pet nohl they llocp Tha rertll ol iu buntu cno Holt C Flaquurcy Find; and Etandurd covial on sandard devlation ol Ihe moant Ino numdut hours 01 eloop (or this sumple Whal perceni tho dala Iias Wunin Draw relalive frequency histogram Andan oqive: Doscribe Ihe s...
2 answers
Provide a set of three distinct numbers a, b, and c such thatand b are not relatively prime b and c are not relatively prime a, b, and c are relatively primeAnswer:
Provide a set of three distinct numbers a, b, and c such that and b are not relatively prime b and c are not relatively prime a, b, and c are relatively prime Answer:...

-- 0.022522--