Plot the function combining an exponential function and a step function

Question

Nick 2022-4-10

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1692900-plot-the-function-combining-an-exponential-function-and-a-step-function

评论： Sam Chak 2022-4-10

采纳的回答： Riccardo Scorretti

untitled.fig

在 MATLAB Online 中打开

I have a funtion involving exponential functions and one exponent is a step function of x.

The plot I need is y vs x,

y=(e^(2t)-1)*e^(-2.5x) ,

and t is a step function of x

where t=x for x<10

t=10 for x>=10

Please help me to plot such a function in xy space.

syms x ;
t =piecewise(x<10,x,x>=10,10);
y=(exp(2*t)-1)*exp(-2.5*x);
fplot(y)

The curve I got from the code above is clearly not correct. Could anyone tell me what is wrong and how to fix it? Thanks!

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Answer 1

Riccardo Scorretti 2022-4-10

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Hi Nick,

Your program seems correct. Perhaps you need to adapt the range over which the graphic is plotted (the default range is [-5 5]). For instance, in the range [0 20] one obtains:

syms x
t = piecewise(x<10, x, x>=10, 10);
y = (exp(2*t)-1) * exp(-2.5*x);         
fplot(y, [0 20], 'LineWidth', 2); % Plot between [0 20]
grid on ; xlabel('x') ; hold on ; drawnow

Let's check it by removing the function t and plotting separately on [0 10] and [10 20]:

y = (exp(2*x)-1) * exp(-2.5*x);

fplot(y, [0 10], 'Color', 'r');

y = (exp(2*10)-1) * exp(-2.5*x);

fplot(y, [10 20], 'Color', 'r');

grid on ; xlabel('x');

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Nick 2022-4-10

Thanks Riccardo! This is exactly what I need.

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Answer 2

Sam Chak 2022-4-10

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1692900-plot-the-function-combining-an-exponential-function-and-a-step-function#answer_939200

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Hi @Nick

Please check the piecewise function

if it is what you desire. Then, check the equation

and the plot.

subplot(2, 1, 1)
fplot(@(x) min(x,10), [-1 15])
grid on
xlabel('x')
ylabel('t')
title('Function t(x)')
subplot(2, 1, 2)
fplot(@(x) (exp(2*min(x, 10))-1).*exp(-2.5*x), [-1 15])
grid on
xlabel('x')
ylabel('y')
title('Function y(x)')