Scaling of a rect function,drawing of signals Im trying to understand on how the drawing of signals (time shifting,scaling...) works. This one example is confusing me, and a bit of help would be much appreciated. This is the starting Signal



We're susposed to give an $x(t)$ expression using rect, dirac and I've done so correctly;

$$x(t) = (t+2) \operatorname{rect}(t/2) + 2\delta(t-2)$$

Now we're susposed to draw a signal $f(t) = x(t/2)$;

And the rect function that is from -1 to 1 only "moves"to 2 and -2, the dirac moves to 4 that makes sense to me, but why doesn't the rect function move to 3 and -3. Thank you
$f(t)$ is just time-stretched $x(t)$ by a factor of 2. Meaning $f(t)$ will take the same value at $t$, which $x(t)$ was taking at $\frac{t}{2}$. So, if the original $rect(t)$ was extending from $-1$ to $1$, then the time-stretched $rect$ will extend from $-2$ to $2$. It can not go from $-3$ to $3$. One thing to keep in mind is that all  time operations (shifting and scaling) will be applied on the independent variable $t$ in $x(t)$. So, 
$$f(t) = x(\frac{t}{2}) = (\frac{t}{2} + 2).rect(\frac{t}{4}) + 2\delta(\frac{t}{2} - 2)$$