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.
