a) plot the graph of 2𝑥 (𝑢(𝑥)−𝑢(𝑥 − 5))+10(𝑢(𝑥 − 5)−𝑢(𝑥 − 10)) for 0 ≤ x ≤ 12. describe the graph produced. in matlab

To plot the given function in MATLAB, you can use the plot() function. However, the given function is a piecewise function, so we need to define it using conditional statements.

Here's how you can plot the graph of the function in MATLAB:

main.m
% Define the function
x = 0:0.1:12;  % Define the range of x values
y = zeros(size(x));  % Preallocate y to store function values

for i = 1:length(x)
    if x(i) >= 0 && x(i) < 5
        y(i) = 10;
    elseif x(i) >= 5 && x(i) < 10
        y(i) = 2 * x(i) + 10;
    elseif x(i) >= 10 && x(i) <= 12
        y(i) = 10;
    end
end

% Plot the graph
plot(x, y)
xlabel('x')
ylabel('f(x)')
title('Graph of 2𝑥 (𝑢(𝑥)−𝑢(𝑥 − 5))+10(𝑢(𝑥 − 5)−𝑢(𝑥 − 10))')
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The resulting graph will produce a step-like function. At x values between 0 and 5, the function will have a constant value of 10. From x values between 5 and 10, the function will be a linear function, increasing from 10 to 2x + 10. Finally, at x values between 10 and 12, the function will have a constant value of 10 again.

Note that I have used a step size of 0.1 in the range of x values to obtain a smoother plot. You can adjust the step size (0.1) and the range of x values (0 and 12) according to your requirements.

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