Hi, i'm just wonder can Matlab have any function to find asymptotes of y = f(x) that satisfy x = x(t) and y = y(t). I have try many solutions but nothing is success.

syms t;

x_t = (t+1)./(t-1);
y_t = (t^2 + 2)./(t^2 - t);

figure;
hold on;
grid on;
fplot(x_t, y_t);

[Mathieu NOE]

see here

Find Asymptotes, Critical, and Inflection Points - MATLAB & Simulink - MathWorks France

[Nhat Huy]

oh ye, i'm also see that post but i'm quite not understand how to find horizontal and vertical aymptotes in x(t) and y(t). For example i have x(t) = (t+1)/(t-1) and y(t) = (t^2 + 2)/(t^2 - t) that satisfy y = f(x), find aymptotes of y =f(x).

[Mathieu NOE]

I don't have the symbolic toolbox , so the best I could get i this numerical approach

t = (-1:1e-3:3);
x_t = (t+1)./(t-1);
y_t = (t.^2 + 2)./(t.^2 - t);
figure(1);
plot(x_t, y_t);
ylim([-30 30]);
hold on

% remove Inf values 
id = (x_t==Inf |  y_t==Inf);
x_t(id) = [];
y_t(id) = [];

% horizontal asymptote
[v1,i1] = min(x_t);
[v2,i2] = max(x_t);
x1 = [v1;v2];
y1 = [y_t(i1);y_t(i2)];
plot(x1, y1,'r--');
% y = ax+b
a = diff(y1)/diff(x1);
b = mean(y1 - a*x1);
eqnH = poly_equation([b a]); % polynomial equation (string)

% vertical asymptote
y_temp = y_t - (a*x_t+b);
[v1,i1] = min(y_temp);
[v2,i2] = max(y_temp);
y2 = [v1;v2];
x2 = [x_t(i1);x_t(i2)];
plot(x2, y2,'g--');
% y = ax+b
a = diff(y2)/diff(x2);
b = mean(y2 - a*x2);
eqnV = poly_equation([b a]); % polynomial equation (string)

legend('data',eqnH,eqnV)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function eqn = poly_equation(a_hat)
eqn = " y = "+a_hat(1);
for i = 2:(length(a_hat))
    
    if sign(a_hat(i))>0
        str = " + ";
    else
        str = " ";
    end
    
    if i == 2
        eqn = eqn+str+a_hat(i)+"*x";
    else
        eqn = eqn+str+a_hat(i)+"*x^"+(i-1)+" ";
    end
end
eqn = eqn+" ";
end

[Nhat Huy]

it works pretty well. Thank you.