(Solved): 1. A "broken-line graph" is defined as a continuous graph composed of linear pieces. (a) Graph the ...

1. A "broken-line graph" is defined as a continuous graph composed of linear pieces. (a) Graph the function \( g(x)=2|x|+|x-3|-x \) without using a calculator and without just plotting a bunch of points and connecting the dots. Your strategy for graphing it should be clear from your work and make use of this way of thinking about the absolute value function: \[ |x|=\left\{\begin{array}{rll} -x & : & x<0 \\ x & : & x \geq 0 \end{array}\right. \] (b) Show that \( f(x)=|x+a|+b x+c \) is a broken-line function (defined as you'd expect: a function whose graph is a broken-line graph).