How to find graph of the sum of two functions












0












$begingroup$


Suppose I know the graphs of two functions $f(x)$ and $g(x)$. How can I find the graph of $h(x)=f(x)+g(x)$? What are the rules to be followed ?



P.S. In case my question seems silly,at least provide me with a link or something so that I can learn!






functions graphing-functions







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$endgroup$












  • $begingroup$
    can you draw $h(x) = f(x) + 2$ ? if so, you already did it for $g(x) = 2$ , can you see how to do it with another $g(x)$ ?
    $endgroup$
    – d_e
    Jul 28 '15 at 16:15










  • $begingroup$
    What about functions with discontinuities?
    $endgroup$
    – user220382
    Jul 28 '15 at 16:17










  • $begingroup$
    use the same logic.
    $endgroup$
    – d_e
    Jul 28 '15 at 16:21
















0












$begingroup$


Suppose I know the graphs of two functions $f(x)$ and $g(x)$. How can I find the graph of $h(x)=f(x)+g(x)$? What are the rules to be followed ?



P.S. In case my question seems silly,at least provide me with a link or something so that I can learn!






functions graphing-functions







share|cite|improve this question











$endgroup$












  • $begingroup$
    can you draw $h(x) = f(x) + 2$ ? if so, you already did it for $g(x) = 2$ , can you see how to do it with another $g(x)$ ?
    $endgroup$
    – d_e
    Jul 28 '15 at 16:15










  • $begingroup$
    What about functions with discontinuities?
    $endgroup$
    – user220382
    Jul 28 '15 at 16:17










  • $begingroup$
    use the same logic.
    $endgroup$
    – d_e
    Jul 28 '15 at 16:21














0












0








0





$begingroup$


Suppose I know the graphs of two functions $f(x)$ and $g(x)$. How can I find the graph of $h(x)=f(x)+g(x)$? What are the rules to be followed ?



P.S. In case my question seems silly,at least provide me with a link or something so that I can learn!






functions graphing-functions







share|cite|improve this question











$endgroup$




Suppose I know the graphs of two functions $f(x)$ and $g(x)$. How can I find the graph of $h(x)=f(x)+g(x)$? What are the rules to be followed ?



P.S. In case my question seems silly,at least provide me with a link or something so that I can learn!






functions graphing-functions




functions graphing-functions






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jul 28 '15 at 16:25









Hoping_Blessing

266212




266212










asked Jul 28 '15 at 16:13







user220382



















  • $begingroup$
    can you draw $h(x) = f(x) + 2$ ? if so, you already did it for $g(x) = 2$ , can you see how to do it with another $g(x)$ ?
    $endgroup$
    – d_e
    Jul 28 '15 at 16:15










  • $begingroup$
    What about functions with discontinuities?
    $endgroup$
    – user220382
    Jul 28 '15 at 16:17










  • $begingroup$
    use the same logic.
    $endgroup$
    – d_e
    Jul 28 '15 at 16:21


















  • $begingroup$
    can you draw $h(x) = f(x) + 2$ ? if so, you already did it for $g(x) = 2$ , can you see how to do it with another $g(x)$ ?
    $endgroup$
    – d_e
    Jul 28 '15 at 16:15










  • $begingroup$
    What about functions with discontinuities?
    $endgroup$
    – user220382
    Jul 28 '15 at 16:17










  • $begingroup$
    use the same logic.
    $endgroup$
    – d_e
    Jul 28 '15 at 16:21
















$begingroup$
can you draw $h(x) = f(x) + 2$ ? if so, you already did it for $g(x) = 2$ , can you see how to do it with another $g(x)$ ?
$endgroup$
– d_e
Jul 28 '15 at 16:15




$begingroup$
can you draw $h(x) = f(x) + 2$ ? if so, you already did it for $g(x) = 2$ , can you see how to do it with another $g(x)$ ?
$endgroup$
– d_e
Jul 28 '15 at 16:15












$begingroup$
What about functions with discontinuities?
$endgroup$
– user220382
Jul 28 '15 at 16:17




$begingroup$
What about functions with discontinuities?
$endgroup$
– user220382
Jul 28 '15 at 16:17












$begingroup$
use the same logic.
$endgroup$
– d_e
Jul 28 '15 at 16:21




$begingroup$
use the same logic.
$endgroup$
– d_e
Jul 28 '15 at 16:21










3 Answers
3






active

oldest

votes


















0












$begingroup$

Since $h(x)=(f+g)(x):=f(x)+g(x)$ for every $x$ in the domain, the graph is the one that you obtain summing the two functions pointwise.



That is, at $x=x_0$ will correspond the point $h(x_0)=f(x_0)+g(x_0)$.



Edited after seeing the comment about discontinuities: if one of the functions $f$ and $g$ has a discontinuity, remember that the domain of $f+g$ is $mathcal {D}_{f+g}=mathcal{D}_f cap mathcal{D}_g$. You can only sum the two functions where they both exists and in these points the same logic applies.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    It's not easy to explain virtually without any graphing instruments, but it's just about summing the two graphs. If you have any questions feel free to ask. Oh, and playing around with Wolfram Alpha's plotting functions should help!
    $endgroup$
    – Lonidard
    Jul 28 '15 at 16:23



















0












$begingroup$

You need to do some analysis.I recommend take the following points.



From basic function f and g:




  1. See when are f and g zero

  2. Find the max and min value of the f and g (example : for sin(x) +1 and -1)


  3. Plot the envelopes of the shape in the enlarged size to get an idea of the graph.



    OR



  4. Calculate the roots of function(sum) if possible.


  5. Analyse the value at the roots.

  6. Find the differential and analyze the differentiability

  7. Find local maxima and minimas and on the basis of differentiability plot the curve.

  8. You may want to analyze the concavity and convexity.For that,find the double differential.


You may like to watch this video.
Curve Sketching






share|cite|improve this answer









$endgroup$





















    0












    $begingroup$

    You can think about the graph of $h(x)$ pointwise, adding the heights of the two graphs $f(x)$ and $g(x)$ at each point $x$. For example, if $f(1) = 2$ and $g(1) = 3$. $$h(1) = f(1) + g(1) = 2 + 3 = 5$$



    Everything is all good now.






    share|cite|improve this answer











    $endgroup$













      Your Answer





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      3 Answers
      3






      active

      oldest

      votes








      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      0












      $begingroup$

      Since $h(x)=(f+g)(x):=f(x)+g(x)$ for every $x$ in the domain, the graph is the one that you obtain summing the two functions pointwise.



      That is, at $x=x_0$ will correspond the point $h(x_0)=f(x_0)+g(x_0)$.



      Edited after seeing the comment about discontinuities: if one of the functions $f$ and $g$ has a discontinuity, remember that the domain of $f+g$ is $mathcal {D}_{f+g}=mathcal{D}_f cap mathcal{D}_g$. You can only sum the two functions where they both exists and in these points the same logic applies.






      share|cite|improve this answer











      $endgroup$













      • $begingroup$
        It's not easy to explain virtually without any graphing instruments, but it's just about summing the two graphs. If you have any questions feel free to ask. Oh, and playing around with Wolfram Alpha's plotting functions should help!
        $endgroup$
        – Lonidard
        Jul 28 '15 at 16:23
















      0












      $begingroup$

      Since $h(x)=(f+g)(x):=f(x)+g(x)$ for every $x$ in the domain, the graph is the one that you obtain summing the two functions pointwise.



      That is, at $x=x_0$ will correspond the point $h(x_0)=f(x_0)+g(x_0)$.



      Edited after seeing the comment about discontinuities: if one of the functions $f$ and $g$ has a discontinuity, remember that the domain of $f+g$ is $mathcal {D}_{f+g}=mathcal{D}_f cap mathcal{D}_g$. You can only sum the two functions where they both exists and in these points the same logic applies.






      share|cite|improve this answer











      $endgroup$













      • $begingroup$
        It's not easy to explain virtually without any graphing instruments, but it's just about summing the two graphs. If you have any questions feel free to ask. Oh, and playing around with Wolfram Alpha's plotting functions should help!
        $endgroup$
        – Lonidard
        Jul 28 '15 at 16:23














      0












      0








      0





      $begingroup$

      Since $h(x)=(f+g)(x):=f(x)+g(x)$ for every $x$ in the domain, the graph is the one that you obtain summing the two functions pointwise.



      That is, at $x=x_0$ will correspond the point $h(x_0)=f(x_0)+g(x_0)$.



      Edited after seeing the comment about discontinuities: if one of the functions $f$ and $g$ has a discontinuity, remember that the domain of $f+g$ is $mathcal {D}_{f+g}=mathcal{D}_f cap mathcal{D}_g$. You can only sum the two functions where they both exists and in these points the same logic applies.






      share|cite|improve this answer











      $endgroup$



      Since $h(x)=(f+g)(x):=f(x)+g(x)$ for every $x$ in the domain, the graph is the one that you obtain summing the two functions pointwise.



      That is, at $x=x_0$ will correspond the point $h(x_0)=f(x_0)+g(x_0)$.



      Edited after seeing the comment about discontinuities: if one of the functions $f$ and $g$ has a discontinuity, remember that the domain of $f+g$ is $mathcal {D}_{f+g}=mathcal{D}_f cap mathcal{D}_g$. You can only sum the two functions where they both exists and in these points the same logic applies.







      share|cite|improve this answer














      share|cite|improve this answer



      share|cite|improve this answer








      edited Jul 28 '15 at 16:27

























      answered Jul 28 '15 at 16:21









      LonidardLonidard

      2,94511021




      2,94511021












      • $begingroup$
        It's not easy to explain virtually without any graphing instruments, but it's just about summing the two graphs. If you have any questions feel free to ask. Oh, and playing around with Wolfram Alpha's plotting functions should help!
        $endgroup$
        – Lonidard
        Jul 28 '15 at 16:23


















      • $begingroup$
        It's not easy to explain virtually without any graphing instruments, but it's just about summing the two graphs. If you have any questions feel free to ask. Oh, and playing around with Wolfram Alpha's plotting functions should help!
        $endgroup$
        – Lonidard
        Jul 28 '15 at 16:23
















      $begingroup$
      It's not easy to explain virtually without any graphing instruments, but it's just about summing the two graphs. If you have any questions feel free to ask. Oh, and playing around with Wolfram Alpha's plotting functions should help!
      $endgroup$
      – Lonidard
      Jul 28 '15 at 16:23




      $begingroup$
      It's not easy to explain virtually without any graphing instruments, but it's just about summing the two graphs. If you have any questions feel free to ask. Oh, and playing around with Wolfram Alpha's plotting functions should help!
      $endgroup$
      – Lonidard
      Jul 28 '15 at 16:23











      0












      $begingroup$

      You need to do some analysis.I recommend take the following points.



      From basic function f and g:




      1. See when are f and g zero

      2. Find the max and min value of the f and g (example : for sin(x) +1 and -1)


      3. Plot the envelopes of the shape in the enlarged size to get an idea of the graph.



        OR



      4. Calculate the roots of function(sum) if possible.


      5. Analyse the value at the roots.

      6. Find the differential and analyze the differentiability

      7. Find local maxima and minimas and on the basis of differentiability plot the curve.

      8. You may want to analyze the concavity and convexity.For that,find the double differential.


      You may like to watch this video.
      Curve Sketching






      share|cite|improve this answer









      $endgroup$


















        0












        $begingroup$

        You need to do some analysis.I recommend take the following points.



        From basic function f and g:




        1. See when are f and g zero

        2. Find the max and min value of the f and g (example : for sin(x) +1 and -1)


        3. Plot the envelopes of the shape in the enlarged size to get an idea of the graph.



          OR



        4. Calculate the roots of function(sum) if possible.


        5. Analyse the value at the roots.

        6. Find the differential and analyze the differentiability

        7. Find local maxima and minimas and on the basis of differentiability plot the curve.

        8. You may want to analyze the concavity and convexity.For that,find the double differential.


        You may like to watch this video.
        Curve Sketching






        share|cite|improve this answer









        $endgroup$
















          0












          0








          0





          $begingroup$

          You need to do some analysis.I recommend take the following points.



          From basic function f and g:




          1. See when are f and g zero

          2. Find the max and min value of the f and g (example : for sin(x) +1 and -1)


          3. Plot the envelopes of the shape in the enlarged size to get an idea of the graph.



            OR



          4. Calculate the roots of function(sum) if possible.


          5. Analyse the value at the roots.

          6. Find the differential and analyze the differentiability

          7. Find local maxima and minimas and on the basis of differentiability plot the curve.

          8. You may want to analyze the concavity and convexity.For that,find the double differential.


          You may like to watch this video.
          Curve Sketching






          share|cite|improve this answer









          $endgroup$



          You need to do some analysis.I recommend take the following points.



          From basic function f and g:




          1. See when are f and g zero

          2. Find the max and min value of the f and g (example : for sin(x) +1 and -1)


          3. Plot the envelopes of the shape in the enlarged size to get an idea of the graph.



            OR



          4. Calculate the roots of function(sum) if possible.


          5. Analyse the value at the roots.

          6. Find the differential and analyze the differentiability

          7. Find local maxima and minimas and on the basis of differentiability plot the curve.

          8. You may want to analyze the concavity and convexity.For that,find the double differential.


          You may like to watch this video.
          Curve Sketching







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Jul 28 '15 at 16:26









          karan kapoorkaran kapoor

          133




          133























              0












              $begingroup$

              You can think about the graph of $h(x)$ pointwise, adding the heights of the two graphs $f(x)$ and $g(x)$ at each point $x$. For example, if $f(1) = 2$ and $g(1) = 3$. $$h(1) = f(1) + g(1) = 2 + 3 = 5$$



              Everything is all good now.






              share|cite|improve this answer











              $endgroup$


















                0












                $begingroup$

                You can think about the graph of $h(x)$ pointwise, adding the heights of the two graphs $f(x)$ and $g(x)$ at each point $x$. For example, if $f(1) = 2$ and $g(1) = 3$. $$h(1) = f(1) + g(1) = 2 + 3 = 5$$



                Everything is all good now.






                share|cite|improve this answer











                $endgroup$
















                  0












                  0








                  0





                  $begingroup$

                  You can think about the graph of $h(x)$ pointwise, adding the heights of the two graphs $f(x)$ and $g(x)$ at each point $x$. For example, if $f(1) = 2$ and $g(1) = 3$. $$h(1) = f(1) + g(1) = 2 + 3 = 5$$



                  Everything is all good now.






                  share|cite|improve this answer











                  $endgroup$



                  You can think about the graph of $h(x)$ pointwise, adding the heights of the two graphs $f(x)$ and $g(x)$ at each point $x$. For example, if $f(1) = 2$ and $g(1) = 3$. $$h(1) = f(1) + g(1) = 2 + 3 = 5$$



                  Everything is all good now.







                  share|cite|improve this answer














                  share|cite|improve this answer



                  share|cite|improve this answer








                  edited Dec 20 '18 at 5:33









                  Karn Watcharasupat

                  3,9742526




                  3,9742526










                  answered Jul 28 '15 at 16:20









                  Paul RegierPaul Regier

                  61




                  61






























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