cost_per_credit.tex

\documentclass{article}

\usepackage{titlesec}
\usepackage{pgfplots}
\usepackage{tikz}
\usepackage{amsmath}

\pgfplotsset{compat=1.18}

\title{Net Cost per Credit with FAFSA}
\author{Jacob Tucker}
\begin{document}
\maketitle
\vspace{-0.5cm}

Let $c$ be the number of credit hours taken in a semester and $a$ be the maximum money awarded by FAFSA. Then $f(c,a)$ represents the money awarded by FAFSA per credit hour taken, $g(c)$ represents the tuition cost per credit hour taken, and $h(c,a)$ represents the net cost per credit hour taken. 

\begin{align}
  f(c,a) &= \begin{cases}
      a, &\text{if } c \geq 12 \\
      0.75a, &\text{if } 9 \leq c < 12 \\
      0.5a, &\text{if } 6 \leq c < 9 \\
      0, &\text{if } c < 6
    \end{cases} \\
  g(c) &= \begin{cases}
    2888.6, &\text{if } c \geq 12 \\
    240.717c, &\text{if } 1 \leq c < 12 \\
    0, &\text{if } c < 1 
    \end{cases} \\
  h(c,a) &= \begin{cases}
    \frac{2888.6 - a}{c}, &\text{if } c \geq 12 \\
    \frac{240.7176c - 0.75a}{c}, &\text{if } 9 \leq c < 12 \\
    \frac{240.7176c - 0.5a}{c}, &\text{if } 6 \leq c < 9 \\
    240.7176, &\text{if } 1 \leq c < 6 \\
    0, &\text{if } c < 1
    \end{cases}
\end{align}
The graph of h(c,1000) is as follows: \\ \\
%f(x) = {(0, x < 1), (240.7176, 1 <= x < 6), ((240.7176 * x - 500) / x, 6 <= x < 9), ((240.7176 * x - 750) / x, 9 <= x < 12), (1888.6 / x, x >= 12)}
\begin{tikzpicture}
  \begin{axis}[scale=1.4, domain=0:20, samples=100, ymin=0, ymax=300, xmin=0, xmax=20, axis lines=middle, xtick={1,6,9,12,20}, ytick={20,40,...,260}, xlabel style={at={(axis description cs:1.05,0)},anchor=west}, ylabel style={at={(axis description cs:-0.1,1)},anchor=south}, xlabel=Credit Hours Taken, ylabel=Cost per Credit, clip=false]
    \addplot[domain=0:1, blue, dashed] {0};
    \addplot[domain=1:6, blue, dashed] {240.7176};
    \addplot[domain=6:9, blue, dashed] {(240.7176*x-500)/x};
    \addplot[domain=9:12, blue, dashed] {(240.7176*x-750)/x};
    \addplot[domain=12:20, blue, dashed] {1888.6/x};
    
    \coordinate (A) at (0,0);
    \coordinate (B) at (1,0);
    \coordinate (C) at (1,240.7176);
    \coordinate (D) at (6,240.7176);
    \coordinate (E) at (6,157.3843);
    \coordinate (F) at (9,185.1620);
    \coordinate (G) at (9,157.3843);
    \coordinate (H) at (12,178.2176);
    \coordinate (I) at (12,157.3843);
    
    \filldraw[black] (A) circle (2pt);
    \filldraw[white, draw=black] (B) circle (2pt);
    \filldraw[black] (C) circle (2pt);
    \filldraw[white, draw=black] (D) circle (2pt);
    \filldraw[black] (E) circle (2pt);
    \filldraw[white, draw=black] (F) circle (2pt);
    \filldraw[black] (G) circle (2pt);
    \filldraw[white, draw=black] (H) circle (2pt);
    \filldraw[black] (I) circle (2pt);
  \end{axis}
\end{tikzpicture}
\end{document}