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Graph Some ideas of
transformations are illustrated. Omnigraph has been used for the
displays but the principles apply to any graphing program. |
The y=f(cx) transformation The
y=cf(x) transformation The
y=f(x)+c transformation The
y=f(x+c) transformation Gradient Rational polynomials Lissajou
figures
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The y=f(cx) transformationThe curve y = (cx)²+(cx)-1 is displayed for various values of c. As c is increased the curve contracts horizontally. This stretching has scale factor 1/c.
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The y=cf(x) transformationThe curve y = c(x²+x-1) is displayed for various values of c. As c is decreased the curve is stretched vertically. The stretch has scale factor c.
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The y=f(x)+c transformationThe curve y = x²+x+c is displayed for various values of c.As c is increased the curve is translated vertically upwards.
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The y=f(x+c) transformationThe curve y = (x+c)²+(x+c)-1 is displayed for various values of c.As c is increased the curve is translated horizontally to the left.
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GradientTangents drawn at various points along a cubic curve show how the gradient changes. |
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Rational polynomialsThe curve of the graph y=1/(x2+c) has either three parts, two parts or one part, depending on the value of the constant c. This animation shows the curve for values increasing from -0.9 through zero to 0.5: |
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Lissajou figuresParametric equations of the form x=sin(f(t)), y=cos(f(t)) produce lissajou figures. Here is a display of one simple case based on x=sin(ct), y=cos(t) for c varying between 1 and 2.
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These animations were produced by GIF Construction Set, which can be downloaded from Alchemy.
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