Adding Dirac Delta with Unit Step
Note that $\delta(t)$ is no function but a distribution. This means that it doesn't have function values but it is only defined by its integral. Consequently, the (generalized) function $x(t)=-\delta(t)+u(t)$ has no value at $t=0$ (the only useful value would be $-\infty$ but that's kind of hard to sketch). For sketching the function graph, you can define function values for $t\neq 0$ in the usual way. At $t=0$ you simply sketch a negative $\delta$-impulse, for $t&lt;0$ the function is zero, and for $t&gt;0$ you assign it the value $1$.