[math] \newcommand{\ex}[1]{\item } \newcommand{\sx}{\item} \newcommand{\x}{\sx} \newcommand{\sxlab}[1]{} \newcommand{\xlab}{\sxlab} \newcommand{\prov}[1] {\quad #1} \newcommand{\provx}[1] {\quad \mbox{#1}} \newcommand{\intext}[1]{\quad \mbox{#1} \quad} \newcommand{\R}{\mathrm{\bf R}} \newcommand{\Q}{\mathrm{\bf Q}} \newcommand{\Z}{\mathrm{\bf Z}} \newcommand{\C}{\mathrm{\bf C}} \newcommand{\dt}{\textbf} \newcommand{\goesto}{\rightarrow} \newcommand{\ddxof}[1]{\frac{d #1}{d x}} \newcommand{\ddx}{\frac{d}{dx}} \newcommand{\ddt}{\frac{d}{dt}} \newcommand{\dydx}{\ddxof y} \newcommand{\nxder}[3]{\frac{d^{#1}{#2}}{d{#3}^{#1}}} \newcommand{\deriv}[2]{\frac{d^{#1}{#2}}{dx^{#1}}} \newcommand{\dist}{\mathrm{distance}} \newcommand{\arccot}{\mathrm{arccot\:}} \newcommand{\arccsc}{\mathrm{arccsc\:}} \newcommand{\arcsec}{\mathrm{arcsec\:}} \newcommand{\arctanh}{\mathrm{arctanh\:}} \newcommand{\arcsinh}{\mathrm{arcsinh\:}} \newcommand{\arccosh}{\mathrm{arccosh\:}} \newcommand{\sech}{\mathrm{sech\:}} \newcommand{\csch}{\mathrm{csch\:}} \newcommand{\conj}[1]{\overline{#1}} \newcommand{\mathds}{\mathbb} [/math]

In each of the following, plot the subset of [math]\R^2[/math] that consists of all pairs [math](x, y)[/math] such that the given equation (or conditions) is satisfied.

• [math]3x + 2y = 3[/math]
• [math]x + y = 1[/math]
• [math]y = |x|[/math]
• [math]y = \sqrt x[/math]
• [math]x^2 + y^2 = 4[/math]
• [math]x^2 + 4y^2 = 4[/math]
• [math]x^2 + y^2 = 1[/math] and [math]y \geq 0[/math]
• [math]4x^2 - y^2 = 4[/math]
• [math]y = 2x^2 + x - 2[/math]
• [math]y = |x^3|[/math]
• [math]y = \mbox{largest integer less than or equal to}\ x[/math]
• [math]y = \begin{cases}2x + 3, & x \geq 0 \\ \frac{x^2}{2}, & x \lt 0.\end{cases}[/math]