Graphing functions with mapping vector vs transformation vector












0












$begingroup$


Teacher 1 method to graph $y=2sqrt[3]{2(x-1)}+4$ says:




  1. Create the transformation vector of $<1,4>$ and plot this point as an ordered pair.

  2. Create a table of values for the parent graph of $y=sqrt[3]x$ using easy, reasonable x values $(-8, -1, 0, 1, 8)$.

  3. To this parent graph table, create 2 new columns and modify the x and y values with the stretch and compression values.

  4. From the plotted ordered pair of $(1,4)$ move over and up according to the new modified values.
    This works and creates correct ordered pairs.


Teacher 2 method:
1. Create a mapping vector of $<1/2 x+1, 2y+4>$




  1. Simply apply these to the parent graph ordered pairs.


teacher 2 method seems simpler. But then I ran into a function that doesn't seem to work with teacher 1 as follows:



$y=2^left(x+1right)-3$.



When I try to create the transformation vector of $<-1,-3>$ I see that this ordered pair is NOT on the graph. So applying the parent graph values to a point NOT on the graph clearly produce erroneous results.

When I use the method of creating $<x-1, y-3$ this works properly.



Why doesn't Teacher method 1 work for this simple exponential?






linear-algebra algebra-precalculus







share|cite|improve this question









$endgroup$












  • $begingroup$
    Isn't this the same as math.stackexchange.com/questions/3027869/… ?
    $endgroup$
    – Gerry Myerson
    Dec 6 '18 at 1:50






  • 1




    $begingroup$
    I deleted the duplicate.
    $endgroup$
    – user163862
    Dec 6 '18 at 6:51
















0












$begingroup$


Teacher 1 method to graph $y=2sqrt[3]{2(x-1)}+4$ says:




  1. Create the transformation vector of $<1,4>$ and plot this point as an ordered pair.

  2. Create a table of values for the parent graph of $y=sqrt[3]x$ using easy, reasonable x values $(-8, -1, 0, 1, 8)$.

  3. To this parent graph table, create 2 new columns and modify the x and y values with the stretch and compression values.

  4. From the plotted ordered pair of $(1,4)$ move over and up according to the new modified values.
    This works and creates correct ordered pairs.


Teacher 2 method:
1. Create a mapping vector of $<1/2 x+1, 2y+4>$




  1. Simply apply these to the parent graph ordered pairs.


teacher 2 method seems simpler. But then I ran into a function that doesn't seem to work with teacher 1 as follows:



$y=2^left(x+1right)-3$.



When I try to create the transformation vector of $<-1,-3>$ I see that this ordered pair is NOT on the graph. So applying the parent graph values to a point NOT on the graph clearly produce erroneous results.

When I use the method of creating $<x-1, y-3$ this works properly.



Why doesn't Teacher method 1 work for this simple exponential?






linear-algebra algebra-precalculus







share|cite|improve this question









$endgroup$












  • $begingroup$
    Isn't this the same as math.stackexchange.com/questions/3027869/… ?
    $endgroup$
    – Gerry Myerson
    Dec 6 '18 at 1:50






  • 1




    $begingroup$
    I deleted the duplicate.
    $endgroup$
    – user163862
    Dec 6 '18 at 6:51














0












0








0





$begingroup$


Teacher 1 method to graph $y=2sqrt[3]{2(x-1)}+4$ says:




  1. Create the transformation vector of $<1,4>$ and plot this point as an ordered pair.

  2. Create a table of values for the parent graph of $y=sqrt[3]x$ using easy, reasonable x values $(-8, -1, 0, 1, 8)$.

  3. To this parent graph table, create 2 new columns and modify the x and y values with the stretch and compression values.

  4. From the plotted ordered pair of $(1,4)$ move over and up according to the new modified values.
    This works and creates correct ordered pairs.


Teacher 2 method:
1. Create a mapping vector of $<1/2 x+1, 2y+4>$




  1. Simply apply these to the parent graph ordered pairs.


teacher 2 method seems simpler. But then I ran into a function that doesn't seem to work with teacher 1 as follows:



$y=2^left(x+1right)-3$.



When I try to create the transformation vector of $<-1,-3>$ I see that this ordered pair is NOT on the graph. So applying the parent graph values to a point NOT on the graph clearly produce erroneous results.

When I use the method of creating $<x-1, y-3$ this works properly.



Why doesn't Teacher method 1 work for this simple exponential?






linear-algebra algebra-precalculus







share|cite|improve this question









$endgroup$




Teacher 1 method to graph $y=2sqrt[3]{2(x-1)}+4$ says:




  1. Create the transformation vector of $<1,4>$ and plot this point as an ordered pair.

  2. Create a table of values for the parent graph of $y=sqrt[3]x$ using easy, reasonable x values $(-8, -1, 0, 1, 8)$.

  3. To this parent graph table, create 2 new columns and modify the x and y values with the stretch and compression values.

  4. From the plotted ordered pair of $(1,4)$ move over and up according to the new modified values.
    This works and creates correct ordered pairs.


Teacher 2 method:
1. Create a mapping vector of $<1/2 x+1, 2y+4>$




  1. Simply apply these to the parent graph ordered pairs.


teacher 2 method seems simpler. But then I ran into a function that doesn't seem to work with teacher 1 as follows:



$y=2^left(x+1right)-3$.



When I try to create the transformation vector of $<-1,-3>$ I see that this ordered pair is NOT on the graph. So applying the parent graph values to a point NOT on the graph clearly produce erroneous results.

When I use the method of creating $<x-1, y-3$ this works properly.



Why doesn't Teacher method 1 work for this simple exponential?






linear-algebra algebra-precalculus




linear-algebra algebra-precalculus






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Dec 6 '18 at 0:58









user163862user163862

88521017




88521017












  • $begingroup$
    Isn't this the same as math.stackexchange.com/questions/3027869/… ?
    $endgroup$
    – Gerry Myerson
    Dec 6 '18 at 1:50






  • 1




    $begingroup$
    I deleted the duplicate.
    $endgroup$
    – user163862
    Dec 6 '18 at 6:51


















  • $begingroup$
    Isn't this the same as math.stackexchange.com/questions/3027869/… ?
    $endgroup$
    – Gerry Myerson
    Dec 6 '18 at 1:50






  • 1




    $begingroup$
    I deleted the duplicate.
    $endgroup$
    – user163862
    Dec 6 '18 at 6:51
















$begingroup$
Isn't this the same as math.stackexchange.com/questions/3027869/… ?
$endgroup$
– Gerry Myerson
Dec 6 '18 at 1:50




$begingroup$
Isn't this the same as math.stackexchange.com/questions/3027869/… ?
$endgroup$
– Gerry Myerson
Dec 6 '18 at 1:50




1




1




$begingroup$
I deleted the duplicate.
$endgroup$
– user163862
Dec 6 '18 at 6:51




$begingroup$
I deleted the duplicate.
$endgroup$
– user163862
Dec 6 '18 at 6:51










1 Answer
1






active

oldest

votes


















1












$begingroup$

I think you know why method 1 didn't work for the exponential. It's because, exactly as you say, $(-1,-3)$ is not on the graph. Use the transformation vector $(-1,-3)$, but apply the parent graph values to the point $(-1,-2)$, which is on the graph, and see if that doesn't work.



Basically, when you strip away everything from the first equation, you're left with $y=root3of x$, which goes through the origin; but when you do the same for the second equation, you get $y=2^x$, which doesn't. That's the difference.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Thank you. I think I will use the second method which always works.
    $endgroup$
    – user163862
    Dec 6 '18 at 17:59











Your Answer





StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");

StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});

function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});


}
});














draft saved

draft discarded


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3027893%2fgraphing-functions-with-mapping-vector-vs-transformation-vector%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown

























1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









1












$begingroup$

I think you know why method 1 didn't work for the exponential. It's because, exactly as you say, $(-1,-3)$ is not on the graph. Use the transformation vector $(-1,-3)$, but apply the parent graph values to the point $(-1,-2)$, which is on the graph, and see if that doesn't work.



Basically, when you strip away everything from the first equation, you're left with $y=root3of x$, which goes through the origin; but when you do the same for the second equation, you get $y=2^x$, which doesn't. That's the difference.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Thank you. I think I will use the second method which always works.
    $endgroup$
    – user163862
    Dec 6 '18 at 17:59
















1












$begingroup$

I think you know why method 1 didn't work for the exponential. It's because, exactly as you say, $(-1,-3)$ is not on the graph. Use the transformation vector $(-1,-3)$, but apply the parent graph values to the point $(-1,-2)$, which is on the graph, and see if that doesn't work.



Basically, when you strip away everything from the first equation, you're left with $y=root3of x$, which goes through the origin; but when you do the same for the second equation, you get $y=2^x$, which doesn't. That's the difference.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Thank you. I think I will use the second method which always works.
    $endgroup$
    – user163862
    Dec 6 '18 at 17:59














1












1








1





$begingroup$

I think you know why method 1 didn't work for the exponential. It's because, exactly as you say, $(-1,-3)$ is not on the graph. Use the transformation vector $(-1,-3)$, but apply the parent graph values to the point $(-1,-2)$, which is on the graph, and see if that doesn't work.



Basically, when you strip away everything from the first equation, you're left with $y=root3of x$, which goes through the origin; but when you do the same for the second equation, you get $y=2^x$, which doesn't. That's the difference.






share|cite|improve this answer









$endgroup$



I think you know why method 1 didn't work for the exponential. It's because, exactly as you say, $(-1,-3)$ is not on the graph. Use the transformation vector $(-1,-3)$, but apply the parent graph values to the point $(-1,-2)$, which is on the graph, and see if that doesn't work.



Basically, when you strip away everything from the first equation, you're left with $y=root3of x$, which goes through the origin; but when you do the same for the second equation, you get $y=2^x$, which doesn't. That's the difference.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Dec 6 '18 at 10:07









Gerry MyersonGerry Myerson

147k8149302




147k8149302












  • $begingroup$
    Thank you. I think I will use the second method which always works.
    $endgroup$
    – user163862
    Dec 6 '18 at 17:59


















  • $begingroup$
    Thank you. I think I will use the second method which always works.
    $endgroup$
    – user163862
    Dec 6 '18 at 17:59
















$begingroup$
Thank you. I think I will use the second method which always works.
$endgroup$
– user163862
Dec 6 '18 at 17:59




$begingroup$
Thank you. I think I will use the second method which always works.
$endgroup$
– user163862
Dec 6 '18 at 17:59


















draft saved

draft discarded




















































Thanks for contributing an answer to Mathematics Stack Exchange!


  • Please be sure to answer the question. Provide details and share your research!

But avoid …



  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.


Use MathJax to format equations. MathJax reference.


To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3027893%2fgraphing-functions-with-mapping-vector-vs-transformation-vector%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







-

Popular posts from this blog

mysqli_query(): Empty query in /home/lucindabrummitt/public_html/blog/wp-includes/wp-db.php on line 1924

Image
0 I just uploaded a new plugin to my wordpress site and I got this warning: mysqli_query(): Empty query in /home/lucindabrummitt/public_html/blog/wp-includes/wp-db.php on line 1924 Usually if I have a problem, I can find answers on google but this one seems pretty particular and I'm not finding any info on it except for this forum. I'm not terribly techie but if someone can tell me how to read this and how to change it I can follow directions pretty well. Thanks All! PS If I don't have the proper tags here could someone add the appropriate tags? php mysql wordpress share | improve this question asked Nov 16 '18 at 20:41 ...
Read more

How to change which sound is reproduced for terminal bell?

Image
3 Recently upgrade to 18.10 from 18.04, and using the terminal is becoming annoying: the new alert sound is a drip ( /usr/share/sounds/gnome/default/alerts/drip.ogg ), and the previous one is still located at ( /usr/share/sounds/ubuntu/stereo/bell.ogg ). My issue is that at the gnome-terminal, when autocompleting or pressing left BOTH sounds are reproduced, at the same time. I want to just have ubuntu/stereo/bell.ogg active, not both . At the moment I have been only able to reduce the volume of the alerts (but still both are played), or turn the alerts down (but I dislike both "solutions"). gnome-terminal 18.10 teminal-bell share | improve this question ...
Read more

Can I use Tabulator js library in my java Spring + Thymeleaf project?

Image
0 I want to add Tabulator js to my java project. I added tabulator.min.js, tabulator.min.css to resources folder. After that added to my html page these dependencies as recommending in readme.md. <link rel="stylesheet" th:href="@{/css/tabulator.min.css}"> <script type="text/javascript" th:src="@{/js/tabulator.min.js}"></script> Now my tables view all elements, that I have in the html page, but not correct. In the documentation of Tabulator is example how to create header and table, var table = new Tabulator("#example-table", { columns:[ {title:"Name", field:"name", sorter:"string", width:200, editor:true}, {title:"Age", field:"age", sorter:"...
Read more