Consider the functions $y(t),f(t)$ and $g(t)$ as drawn, and respond the questions:

a$)$ Write a mathematical expression for the signals $y(t)$ and $f(t)$ using the unit step function $u(t).$

b$)$ Draw the function $z(t)=y(t)+f(t).$

c$)$ Draw the function $w(t)=y(t)*f(t).$

d$)$ Draw the function $g(t)=2f(1-2t)+4.$