You are asking about nonlinear fitting and several choices are available including nlinfit. Try can try using Curve Fitter, from the Apps tab. Select for data your x and say y1. The functions you mention are available options. Custom ones are also possible. Pick say exponential and you will see the R^2 at the lower right. Export code and you get the attached as a template for nonlinear fitting. The R^2 value will be found in returns fitresult and gof. You could just build a set of five functions to perform fits for each functional form and then just called them with different y values. Be aware though that nonlinear fitting requires input parameter guesses so such fits can fail. Also, your functions can have different numbers of parameters, e.g. any number for generic polynomial fits. The number of degrees of freedom is important in interpreting R^2.
function [fitresult, gof] = createFit1(x, y1)
%CREATEFIT1(X,Y1)
% Create a fit.
%
% Data for 'untitled fit 1' fit:
% X Input: x
% Y Output: y1
% Output:
% fitresult : a fit object representing the fit.
% gof : structure with goodness-of fit info.
%
% See also FIT, CFIT, SFIT.
% Auto-generated by MATLAB on 28-Apr-2023 19:27:20
%% Fit: 'untitled fit 1'.
[xData, yData] = prepareCurveData( x, y1 );
% Set up fittype and options.
ft = fittype( 'exp1' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [0.00698176628929166 1.20905013311468];
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts );
% Plot fit with data.
figure( 'Name', 'untitled fit 1' );
h = plot( fitresult, xData, yData );
legend( h, 'y1 vs. x', 'untitled fit 1', 'Location', 'NorthEast', 'Interpreter', 'none' );
% Label axes
xlabel( 'x', 'Interpreter', 'none' );
ylabel( 'y1', 'Interpreter', 'none' );
grid on
