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

#let b2_1 = cetz.canvas(length: 1.25cm,{
    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(
    //definitionen
    name: "plot",
    size: (6, 6),
    x-tick-step: none,
    y-tick-step: none,
    axis-style: "school-book",
    x-label: $x$,
    y-label: $y$,
    x-ticks: ((0.5, $1/2$),(1.25, $x$),),
    y-ticks: ((0.25, $1/4$),(1.5625, $x^2$),),
    {
    //berechnungen und plot
    let f = x => calc.pow(x, 2)
    let x0 = 0.5
    let y0 = f(x0)
    let x1 = 1.25
    let y1 = f(x1)
    // Berechnung der Steigung m = (y1 - y0) / (x1 - x0)
    let m = (y1 - y0) / (x1 - x0)
    
      
    // Sekantenfunktion: s(x) = m * (x - x0) + y0
    let s = x => m * (x - x0) + y0

    let x1_1 = x1 + 0.1
    let x0_1 = x0 - 0.2
    let y0_1 = y0 + 0.2
    let x2 = ((x1 - x0)/2) + x0
    let y3 = ((y1 - y0)/2) +y0
    
    plot.add(x => calc.pow(x, 2), domain: (-1.4, 1.8))
    //Sekante
    plot.add(s, domain: (0.3, 1.7), style: (stroke: red))
    plot.add-anchor("pt1", (-1.4,y1))
    plot.add-anchor("P", (x1_1,y1))
    plot.add-anchor("P0", (x0_1,y0_1))

    plot.add-anchor("F1", (x2,0.14))
    plot.add-anchor("F2", (x1+0.1,y3))

    
    plot.add(((x0, 0), (x0, y0)), style: (stroke: (dash: "dashed", paint: gray, thickness: 0.75pt)))
    plot.add(((x1, 0), (x1, y1)), style: (stroke: (dash: "dashed", paint: gray, thickness: 0.75pt)))
    plot.add(((0, y1), (x1, y1)), 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), (x1, y0)), style: (stroke: ( paint: gray.darken(80%), thickness: 0.5pt)))
    plot.add(((x1, y0), (x1, y1)), style: (stroke: ( paint: gray.darken(80%), thickness: 0.5pt)))

    
    plot.add(((x0, y0),), mark: "o")
    plot.add(((x1, y1),), mark: "o")

    
    
    }
  )
  //Der Plot muss einen Namen haben
    content("plot.pt1", text(0.85em)[$y=x^2$], anchor: "east", name: "pt")
    content("plot.P", text(0.75em)[$P$], anchor: "west", name: "p")
    content("plot.P0", text(0.75em)[$P_0$], anchor: "west", name: "p0")
    content("plot.F1", text(0.75em)[$x- 1/2$], anchor: "center", name: "f1")
    content("plot.F2", text(0.75em)[$x^2- 1/4$], anchor: "west", name: "f2")
})

#let b2_2 =  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")
})

#let b2_3 = cetz.canvas(length: 3cm, {
  import cetz.draw: *

  set-style(
    mark: (fill: black, scale: 2),
    stroke: (thickness: 0.4pt, cap: "round"),
    angle: (
      radius: 0.3,
      label-radius: .22,
      fill: green.lighten(80%),
      stroke: (paint: green.darken(50%))
    ),
    content: (padding: 1pt)
  )

 //grid((-.25, -.25), (2, 2 ), step: 0.5, stroke: gray + 0.2pt)

  line((0, 0.25), (3, 0.25), mark: (end: "stealth", scale: 0.8))
  content((), $ x $, anchor: "west")

  line((0.5,0.25),(2.5,0.25), stroke: 2pt)
  
  circle((0.5,0.25), radius: 0.025, fill: white, stroke: (paint: black, thickness: 1.25pt), name: "01")
  
  //content("01.end", anchor: "north", padding: (left: 3mm, bottom: 2mm),  text(green.darken(30%))[Punkt $(a_1, a_2)$])

  content("01.south", padding: (left: 0mm, bottom: -5mm),  text([$x_0 -c$]))

  circle((1.5,0.25), radius: 0.025, fill: white, stroke: (paint: black, thickness: 1.25pt), name: "02")

  content("02.south", padding: (left: 0mm, bottom: -5mm),  text([$x_0$]))

  circle((2.5,0.25), radius: 0.025, fill: white, stroke: (paint: black, thickness: 1.25pt), name: "03")

  content("03.south", padding: (left: 0mm, bottom: -5mm),  text([$x_0 +c$]))

  circle((1.5,0), radius: 0.0005, fill: white, stroke: (paint: white, thickness: 1.25pt), name: "02")

})

#let b2_4 = cetz.canvas({
    import cetz.draw: *
    //import cetz-plot: *
    
    let f = x => (calc.pow(x,3)+0.5)
    let x1 = 0.35
    let x3 = 0.5
    let x0 = 0.7
    let x2 = 0.8
    let y1 = f(x1)
    
    
    plot.plot(size: (6,7), name: "plot", axis-style: "school-book", x-tick-step:none, y-tick-step:none, x-label: $x$,
    y-label: $y$,
    x-ticks: ((x1, $x_1$),(x3, $x_3$),(x0, $x_0$),(x2, $x_2$),),
    y-ticks: ((f(x1), $f(x_1)$),(f(x2), $f(x_2)$),(f(x0), $g$),(f(x3), $f(x_3)$)), {
    plot.add(domain: (0.25, 1), f, style: (stroke: red))

       
        
        // Hilfslinie damit Koordinatensystem nicht verrutscht
    plot.add(((0, 0), (0, 0.1)), style: (stroke: none)) 
    //circle((x1, y1), radius: 0.05, fill: black)


    plot.add(((x1, 0), (x1, f(x1))), style: (stroke: (dash: "dashed", paint: gray, thickness: 1pt)))
    plot.add(((0, f(x1)), (x1, f(x1))), style: (stroke: (dash: "dashed", paint: gray, thickness: 1pt)))
    
    plot.add(((x3, 0), (x3, f(x3))), style: (stroke: (dash: "dashed", paint: gray, thickness: 1pt)))
    plot.add(((0, f(x3)), (x3, f(x3))), style: (stroke: (dash: "dashed", paint: gray, thickness: 1pt)))
    
    plot.add(((x0, 0), (x0, f(x0))), style: (stroke: (dash: "dashed", paint: gray, thickness: 1pt)))
    plot.add(((0, f(x0)), (x0, f(x0))), style: (stroke: (dash: "dashed", paint: gray, thickness: 1pt)))
    
    plot.add(((x2, 0), (x2, f(x2))), style: (stroke: (dash: "dashed", paint: gray, thickness: 1pt)))
    plot.add(((0, f(x2)), (x2, f(x2))), style: (stroke: (dash: "dashed", paint: gray, thickness: 1pt)))

    plot.add(((x1, f(x1)),), mark: "o", mark-style:(stroke: (paint: black, thickness: 0.75pt), fill: black))
    plot.add(((x3, f(x3)),), mark: "o", mark-style:(stroke: (paint: black, thickness: 0.75pt), fill: black))
    plot.add(((x0, f(x0)),), mark: "o", mark-style:(stroke: (paint: black, thickness: 0.75pt), fill: white))
    plot.add(((x2, f(x2)),), mark: "o", mark-style:(stroke: (paint: black, thickness: 0.75pt), fill: black))

    plot.add-anchor("F", (x2 + 0.1,f(x2)))
    })

    content("plot.F", text(0.85em)[$y=x^2$], anchor: "west", name: "pt")
    
    
})