Plot two functions in one diagramm with different y-axis limits

Does someone know how i could solve the following Problem:

%x_1,...,x_7 are real valued Variables (which are generated before)
g = 0.5*x_1*(x_2*f_1-x_3*f_2)^2+x_4*f_1+x_5*f_2+x_6-x_7; 
funct = solve(g,f_2,'Real',true,'ReturnConditions',true);

y_lim = [10,15];
syms f_1
assume(funct.conditions);

funct.f_2(isAlways(funct.f_2 < y_lim(1),Unknown="falseWithWarning")) = NaN;
funct.f_2(isAlways(funct.f_2 > y_lim(2),Unknown="falseWithWarning")) = NaN;

fplot(funct.f_2, [7,50] ,'Color', 'b');

So i want to plot the quadratic function "funct" in the y-Intervall [10,15] and x-Intervall [7,50] but i get the (4) Warnings:

Warning: Unable to prove '(423*f_1)/77 - (576460752303423488000000*(7353528183219767092002251709184784741/324518553658426726783156020576256000000 -
(907661965900503303521461870041895139*f_1)/16615349947311448411297588253504307200000)^(1/2))/18611613717480648557 -
86464670358732992000000/18611613717480648557 < 10'. 
> In symengine
In sym/isAlways (line 41)

So the function gets plottet and the x-Interval is respected, but not the y-Interval. If i set Unknown="true" my function is not plotted at all. Do you know how i could plot the function "funct" correctly (in both intervals)? Thanks

Answer 1

[Jaswanth]

Hi,

To plot two functions with different y-axis limits in MATLAB, you can use two y-axes on the same plot with the “yyaxis” function.

Assuming you are solving for (f_2) in terms of (f_1), use “fplot” to plot the functions over the specified x-interval.

Next, use the “yyaxis” function with “yyaxis left” and “yyaxis right” to create two y-axes, one for each function, switching between the left and right y-axes. Use “ylim” to set the y-axis limits for each axis.

Please refer to the following example to structure the code for plotting two functions with different y-axis limits:

% Define symbolic variables
syms f_1 f_2;

% Define your equation
x_1 = 1; x_2 = 2; x_3 = 3; x_4 = 4; x_5 = 5; x_6 = 6; x_7 = 7; % Example values
g = 0.5*x_1*(x_2*f_1-x_3*f_2)^2 + x_4*f_1 + x_5*f_2 + x_6 - x_7;

% Solve for f_2
funct = solve(g, f_2, 'Real', true, 'ReturnConditions', true);

% Assume conditions
assume(funct.conditions);

% Define y-axis limits
y_lim1 = [10, 15]; % Limits for first function
y_lim2 = [0, 20];  % Limits for second function (example)

% Create figure
figure;

% Plot first function
yyaxis left;
fplot(funct.f_2, [7, 50], 'Color', 'b');
ylim(y_lim1);
ylabel('f_2 Values');

% Plot second function (for demonstration, using a simple example function)
yyaxis right;
fplot(@(f_1) sin(f_1), [7, 50], 'Color', 'r');
ylim(y_lim2);
ylabel('sin(f_1)');

% Add labels and title
xlabel('f_1 Values');
title('Plot with Two Y-Axes');

% Add legend
legend('f_2', 'sin(f_1)');

Kindly refer to the following MathWorks documentation to know more about the functions discussed above:

• yyaxis: https://www.mathworks.com/help/matlab/ref/yyaxis.html
• ylim: https://www.mathworks.com/help/matlab/ref/ylim.html

I hope the solution provided above is helpful.