#import "@preview/cetz:0.4.2"
#import "@preview/cetz-plot:0.1.3": plot

#cetz.canvas({
  
    import cetz.draw: *
    set-style(
    axes: (
      // Basisstil beibehalten
      stroke: (thickness: 0.5pt),
      // x-Achse: stealth-Pfeil am Ende
      x: (mark: (end: "stealth", fill: black)),
      // y-Achse: stealth-Pfeil am Ende
      y: (mark: (end: "stealth", fill: black)),
    ),
  )
  plot.plot(
    name: "plot",
    size: (5, 5),
    x-tick-step: none,
    y-tick-step: none,
    axis-style: "school-book",
    x-label: $x$,
    y-label: $y$,
    x-ticks: ((0.5, $1/2$),),
    y-ticks: ((1, $1$),),
    
 //definitionen
    {
      let f = x => if x != 0.5 { (calc.pow(x, 2) - 0.25) / (x - 0.5) } else { none }
      let x0 = 0.5
      let y0 = 1
    plot.add(f, domain: (-0.6, 0.75), style: (stroke: blue))

    plot.add(((x0, 0), (x0, y0)), style: (stroke: (dash: "dashed", paint: gray, thickness: 0.75pt)))

    plot.add(((0, y0), (x0, y0)), style: (stroke: (dash: "dashed", paint: gray, thickness: 0.75pt)))

    plot.add(((x0, y0),), mark: "o")
  
    plot.add-anchor("F1", (-.7,0.5))
    plot.add-anchor("F2", (-.7,0.35))
    }
  )
    content("plot.F1", text(0.85em)[$y=(x^2-1/4)/(x-1/2)$], anchor: "west", name: "pt")
    content("plot.F2", text(0.85em)[$(x eq.not 1/2)$], anchor: "west", name: "pt")
})