Drawing unit step function

Question

I am having problem to draw function when signal is given. Here, I understand first (ramp function at $t=0$), but can someone explain me second and thirs? What this $-2$ is telling me? $(t-1)$ means that there is change at t=1, but what about rest?

Answer 1

The first term is alone from $0$ to $1$ and has a slope $\color{skyblue}1$.

The second term enters into play from $1$ and adds a slope $-2$, for a total of $\color{forestgreen}{-1}$.

The third term enters into play from $2$ and makes the slope $\color{orange}0$.

So the piecewise signal goes through points $(0,0),(1,1),(2,0)$, then is horizontal.