assignment Homework
Static Fields 2023 (6 years)
The function \(\theta(x)\) (the Heaviside or unit
step function) is a defined as:
\begin{equation}
\theta(x) =\begin{cases}
1 & \textrm{for}\; x>0 \\
0 & \textrm{for}\; x<0
\end{cases}
\end{equation}
This function is discontinuous at \(x=0\) and is generally taken to
have a value of \(\theta(0)=1/2\).
Make sketches of the following functions, by hand, on axes with the
same scale and domain. Briefly describe, using good scientific
writing that includes both words and equations, the role that the
number two plays in the shape of each graph:
\begin{align}
y &= \theta (x)\\
y &= 2+\theta (x)\\
y &= \theta(2+x)\\
y &= 2\theta (x)\\
y &= \theta (2x)
\end{align}