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

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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.

Accepted Answer

Star Strider
Star Strider on 30 Jul 2015
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
  1 Comment
Star Strider
Star Strider on 30 Jul 2015
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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More Answers (1)

Jon
Jon on 30 Jul 2015
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:
  2 Comments
Mark Dillon
Mark Dillon on 30 Jul 2015
I could do it that way, but I need to do it using zero somehow in an for or while loop.
Jon
Jon on 30 Jul 2015
Edited: Jon on 30 Jul 2015
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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