The problem asks to draw the graphs of several piecewise-defined functions. We will focus on function a), which is given by: $f(x) = \begin{cases} x, & x < 0 \\ 0, & x = 0 \\ 2x, & x > 0 \end{cases}$

1. Problem Description

The problem asks to draw the graphs of several piecewise-defined functions. We will focus on function a), which is given by:

$f(x) = \begin{cases} x, & x < 0 \\ 0, & x = 0 \\ 2x, & x > 0 \end{cases}$

2. Solution Steps

To draw the graph of this function, we consider each part separately:

* For $x < 0$, $f(x) = x$. This is a straight line with a slope of 1 and passes through the origin. Since it's defined only for $x < 0$, it's a ray extending from the origin into the negative x-axis. Note that the origin itself is not included, but $f(x)$ approaches to $0$ as $x$ approaches to $0$ from left side.

* For $x = 0$, $f(x) = 0$. This is just a single point at the origin (0, 0).

* For $x > 0$, $f(x) = 2x$. This is a straight line with a slope of 2 and passes through the origin. Since it's defined only for $x > 0$, it's a ray extending from the origin into the positive x-axis. Note that the origin itself is not included, but $f(x)$ approaches to $0$ as $x$ approaches to $0$ from right side.

The graph consists of a ray with slope 1 for $x<0$, the point (0,0), and a ray with slope 2 for $x>0$.

3. Final Answer

The graph of the function consists of three parts: a line $y=x$ for $x<0$, the point (0,0), and a line $y=2x$ for $x>0$.