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Published byCelia Burwell Modified over 2 years ago

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Transformations of graphs Summary of the four types of transformation

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y = f(x) Y = f(x) is any function or equation of a graph. This example is an cubic function/equation. There are five basic types of transformation of a graph i.e. five ways we can move the graph or change its shape

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y = f(x) This is a ‘shift’ in the y-direction y = f(x) + a +a y = f(x) + a Point (x, y) becomes point (x, y+a)

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y = f(x) This is a ‘shift’ in the x-direction, opposite to the sign of number a y = f(x+a) -a y = f(x+a) Point (x, y) becomes point (x-a, y)

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y = f(x) This is a ‘reflection’ in the axis, mirror line y = 0 Every y coordinate gets multiplied by -1 y = -f(x)

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y = f(x) This is a ‘stretch’ in the y-direction, Scale factor A. Every answer (y-coordinate) gets multiplied by A y = Af(x) Notice what happens at the zeros

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y = f(x) This is a ‘stretch’ in the x-direction, Scale factor 1 / A Every x coordinate gets multiplied by 1 / A, y values stay the same y = f(Ax) Notice what happens at the y-intercept y = f(Ax)

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One missing transformation What about f(-x) f(x)=x 3 -3x-1 Reflection across the y axes

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