shifting and time reversal of a piecewise defined signal

I have a piece-wise defined function x(t) as shown below. I need to plot x(-t-1) now but am not sure how to do it. I tried to create a function like "modified_x= @x x(-t-1) but it only returns a horizontal line at x(t)=0. Please help gurus! below is my code that gives me my desired function of t. Now I need to apply x(-t-1).

Answer 1

[Walter Roberson]

x = @(t) (0 <= t & t < 2) .* exp(t)/2 + (2 <= t & t < 4) .* (2*t-8);
shifted_x = @(t) x(-t-1);

t = linspace(-6, 0);

plot(t, shifted_x(t))
xlabel('Time(t)')
ylabel('x(t)');

Reversal around time t = c would be x(c-t) so you are reversing around t = -1 and that means that anything that used to happen at time 2 would now happen at time -3, anything time 3 would now happen at -4 and so on, so your primary problem was that you were looking in the wrong time range and you were cutting out the interesting parts of the plot with your axis() call.

[Walter Roberson]

If you want to reverse around time t = c and have that still map into time t = c, then the formula is

c = 1;
shifted_x = @(t) x(2*c-t);

[Aaron Connell]

any way to cut off the function at t=-1? It looks as if it does a little drop and then a flat line up to zero

[Walter Roberson]

Change the linspace bounds for t.