Transforming a graph

One parent function, four sliders, and the shape that results. Every slider maps to one word: stretch, shift, squeeze, raise.

examples/showcase-transformations.axis

config {
    showGrid: true
    xAxisStep: 1
    yAxisStep: 1
}

"y = a * f(b * (x - h)) + k"

folder "Sliders" {
    a = 1 @ slider: -3..3 step 0.1
    b = 1 @ slider: -3..3 step 0.1
    h = 0 @ slider: -6..6 step 0.1
    k = 0 @ slider: -6..6 step 0.1
}

"The parent function - swap x^2 for sin(x), abs(x) or sqrt(x)."

f(x) = x ^ 2 @ hidden

f(x) @ color: BLACK, lineWidth: 2, lineOpacity: 0.3, lineStyle: DASHED

"The transformed one."

g(x) = a * f(b * (x - h)) + k @ color: PURPLE, lineWidth: 4

folder "What each slider does" {
    "a stretches vertically, and flips when negative."
    "b squeezes horizontally, and flips when negative."
    "h shifts right, k shifts up."
    "The image of the parent's vertex."
    (h, k) @{
        color: PURPLE
        pointSize: 16
        label: "(h, k)"
        showLabel
        labelOrientation: above_right
    }
}

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