How do I plot the intersections of two functions???

Question

Mark Dillon 2015-7-30

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评论： Star Strider 2015-7-30

I have been tasked with plotting two functions and having to find where the two intersect. I also have to use a for or while loop to automatically find all of the intersections in the given domain. And print the results of those intersections.

This is what I have worked out so far, but I cannot figure out how to show the intersections.

if true
  %  code
    %%Find all of the intersections of two functions in the domain of x
     % Variable 3 ≤ x ≤ 8
    % Functions
    F1 = @(x) 90.*exp(-x) - 1;
    F2 = @(x) sin(2.*pi.*x);
    fplot(F1,[3,8]);
    grid on;
    hold on;
    fplot(F2,[3,8]);
  end

[EDIT] Here are a couple hints I have been given:

Hint 1: How do you make an anonymous function that takes one variable (x) and returns zero when the two functions intersect?

Hint 2: You need to call fzero a bunch of times with a reasonable set of guesses, enough to make sure that you actually get all of the intersections. Each time you calculate a new intersection, compare it to ALL of the intersections that you have already calculated. If the difference between the new intersection and any of the old ones is very small (<0.00006), do not add it to your list and just move on to calculating the next one. Don’t forget to check that the intersection is in the given domain.

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Answer 1

Star Strider 2015-7-30

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One possibility:

F1 = @(x) 90.*exp(-x) - 1;
F2 = @(x) sin(2.*pi.*x);
x = linspace(3, 8, 500);                                % Domain ‘x’
fcndif = @(x) F1(x) - F2(x);                            % Function Differences
zx = fcndif(x) .* circshift(fcndif(x), [0 -1]);         % Detect Zero-Crossings
gues = find(zx <= 0);                                   % Find Indices Of Zero Crossings
for k1 = 1:length(gues)
    intsct(k1) = fzero(fcndif, x(gues(k1)));            % Find ‘x’ at Zero Crossings
end
figure(1)
plot(x, F1(x),  x, F2(x))
hold on
plot(intsct, F1(intsct), 'bp')
hold off
grid

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Star Strider 2015-7-30

在 MATLAB Online 中打开

Improved version:

F1 = @(x) 90.*exp(-x) - 1;
F2 = @(x) sin(2.*pi.*x);
x = linspace(3, 8, 150);                                % Domain ‘x’
fcndif = @(x) F1(x) - F2(x);                            % Function Differences
zx = fcndif(x) .* circshift(fcndif(x), [0 -2]);         % Detect Zero-Crossings
gues = find(zx <= 0);                                   % Find Indices Of Zero Crossings
for k1 = 1:length(gues)
    intsct(k1) = fzero(fcndif, x(gues(k1)));            % Find ‘x’ at Zero Crossings
end
intsct = unique(round(intsct*10^6)./10^6);
figure(1)
plot(x, F1(x),  x, F2(x))
hold on
plot(intsct, F1(intsct), 'bp')
hold off
grid

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Answer 2

Jon 2015-7-30

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I don't know if there's a built-in code for finding intersections from function objects, but you could use the intersections.m function from the FEX.

      rng = 3:.05:8;
      f1 = F1(rng);
      f2 = F2(rng);
      [xints,yints,~,~] = intersections(rng,f1,rng,f2,1);
      hold on
      plot(xints,yints,'r*')

will result in the following image:

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Mark Dillon 2015-7-30

I could do it that way, but I need to do it using zero somehow in an for or while loop.

Jon 2015-7-30

编辑：Jon 2015-7-30

Oh, I didn't realize I was doing your homework. You want to find when F1 = F2 (i.e., their intersection). Just rearrange the equation and you see that F1-F2=0 (at their intersection). Now you have a new function (F1-F2) whose roots are the intersections of F1 with F2. The hints basically spell it out.

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