How to get the output of a signal given the input and impulse Here is my question
So given the input and impulse response how would I go about getting the output? The output is given in solution (in teal) but I have no idea how to get it .
thanks
 A: It's been a long time since I did any work with impulse functions, transfer functions and the like, and I have never seen an impulse response which started before the impulse (i.e. non-causal), but I can see how the answer here was arrived at. 
The impulse response is the output of a system when the system is subjected to an impulse and the impulse, unless otherwise stated, is the Dirac delta function $\delta(t)$ which occurs at $t = 0$. The impulse response in your first graph is thus the result of the input $x(t) = \delta(t)$. This input would be shown on your first graph as an arrow of height $1$ pointing up at $t = 0$. 
You are now given a new input of $x(t) = -2\delta(t+5)$. This is again a Dirac delta function but with a negative scale factor and a time shift. Since an impulse response completely determines the transfer function of a system, you only need to do the same scale factoring and time shift of the output as was done to the input. I.e. take the impulse response in the first graph, time shift it backwards $5$ units and multiply it by the scale factor $-2$. 
