There are several lines created for the first plot call. Return handles to each plot call and then choose the first line of each as the axis argument array to the legend call —
f = @(x) 2.^x .* log(2).^0;
f_prime1 = @(x) 2.^x .* log(2).^1;
f_prime2 = @(x) 2.^x .* log(2).^2;
f_prime3 = @(x) 2.^x .* log(2).^3;
% Taylor series (polynomials) are declared as anonymous functions
% x0 : expansion point
% x : the point at which I would like to evaluate the Taylor series
%% 0th order Taylor series
T0 = @(x0,x) f(x0);
% 1st order Taylor series
T1 = @(x0,x) f(x0) + f_prime1(x0)*(x-x0);
% 2nd order Taylor series
T2 = @(x0,x) f(x0) + f_prime1(x0)*(x-x0) + f_prime2(x0)*(x-x0).^2/2;
% 3rd order Taylor series
T3 = @(x0,x) f(x0) + f_prime1(x0)*(x-x0) + f_prime2(x0)*(x-x0).^2/2 + f_prime3(x0)*(x-x0).^3/6;
%%
x0 = 1;
% Plot the Taylor series T0, T1, T2, T3 between -5 <= x <= +5 using expansion point x0 = 1;
x = linspace(-5,5,60);
y0 = T0(x0,x);
y1 = T1(x0,x);
y2 = T2(x0,x);
y3 = T3(x0,x);
yTrue = f(x);
%%
figure
hp{1} = plot(x,y0,'-ob','LineWidth',2);
hold on
hp{2} = plot(x,y1,'-ok','LineWidth',2);
hold on
hp{3} = plot(x,y2,'-or','LineWidth',2);
hold on
hp{4} = plot(x,y3,'-og','LineWidth',2);
hold on
hp{5} = plot(x,yTrue,'-oc','LineWidth',2);
xlabel('x')
ylabel('y')
legend([hp{1}(1);hp{2}(1);hp{3}(1);hp{4}(1);hp{5}(1)], 'T0','T1','T2','T3','f(x) = 2^x')
set(gca, 'FontSize',18)
grid on
EDIT — Clarified explanation.
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