Functions

examples/02-functions.axis

config {
    showGrid: true
}

"Functions"

// f(x) = ... defines a function. It graphs, and it can be called elsewhere.
f(x) = x ^ 2 - 4x + 3 @ color: RED
g(x) = 2x - 1 @ color: BLUE

// Composition is just a call inside a call.
h(x) = f(g(x)) @ color: GREEN, lineStyle: DASHED

// A function of two arguments does not graph on its own - it is a helper.
rectArea(w, h) = w * h @ hidden

folder "Trigonometry" {
    y = sin(x) @ color: RED
    y = cos(x) @ color: BLUE
    y = tan(x) @ color: GREEN, lineOpacity: 0.5
    y = arctan(x) @ color: PURPLE, lineStyle: DASHED
    y = tanh(x) @ color: ORANGE
    "The inverse hyperbolics: arcsinh undoes sinh."
    y = arcsinh(x) @ color: ORANGE, lineStyle: DASHED
}

folder "Powers and roots" {
    y = sqrt(x) @ color: RED
    y = nthroot(x, 3) @ color: BLUE
    y = exp(x) @ color: GREEN
    y = ln(x) @ color: PURPLE
    y = log(x) @ color: ORANGE
    y = log(x, 2) @ color: ORANGE, lineStyle: DASHED
}

folder "Calculus" {
    "f's slope, its second derivative, and the area under it from 0 to x."
    y = f'(x) @ color: RED, lineStyle: DASHED
    y = d/dx f'(x) @ color: RED, lineStyle: DOTTED
    y = int(t = 0..x, f(t)) @ color: BLUE
    "The first six terms of the series for e^x, beside the real thing."
    y = sum(k = 0..5, x ^ k / k!) @ color: GREEN
    y = exp(x) @ color: GREEN, lineStyle: DASHED
    s = sum(n = 1..100, 1 / n ^ 2) @ hidden
    p = prod(n = 1..5, n) @ hidden
}

folder "Rounding and sign" {
    y = floor(x) @ color: RED
    y = ceil(x) @ color: BLUE
    y = round(x) @ color: GREEN
    y = sign(x) @ color: PURPLE
    y = abs(x) @ color: ORANGE
    "The error function, which has no closed form."
    y = erf(x) @ color: RED, lineStyle: DASHED
}

folder "Recursion" {
    "A function may call itself, and its base cases say where that stops."
    fib(n) = fib(n - 1) + fib(n - 2) with fib(0) = 0, fib(1) = 1 @ hidden
    tri(n) = tri(n - 1) + n @ hidden
    tri(1) = 1 @ hidden
    F = fib(10) @ hidden
    T = tri(10) @ hidden
}

folder "Number theory" {
    y = mod(x, 3) @ color: RED
    d = gcd(12, 18) @ hidden
    m = lcm(4, 6) @ hidden
    y = factorial(3) @ hidden
    "gcd(12, 18) and lcm(4, 6) evaluate in the expression list."
}

Open in playground →