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Transforming Functions

Transforming Functions. Reflection. Assuming we know the shape and form of the graph of y = f(x) …. … The graph of y = -f(x) is a reflection of this graph in the x-axis. Look at the example below – graphs of y = x 2 and y = -(x 2 ). Reflection … (continued).

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Transforming Functions

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  1. Transforming Functions

  2. Reflection Assuming we know the shape and form of the graph of y = f(x) …. … The graph of y = -f(x) is a reflection of this graph in the x-axis Look at the example below – graphs of y = x2 and y = -(x2)

  3. Reflection … (continued) Assuming we know the shape and form of the graph of y = f(x) …. … The graph of y = f(-x) is a reflection of this graph in the y-axis Look at the example below – graphs of y = 2x and y = 2-x

  4. Stretch Assuming we know the shape and form of the graph of y = f(x) …. … The graph of y = af(x) is a stretchof this graph vertically by a factor of a Look at the example below – graphs of y = cosxand y = 3cosx

  5. Stretch (continued) Assuming we know the shape and form of the graph of y = f(x) …. … The graph of y = af(ax) is a compressionof this graph horizontally by a factor of a (usually called a stretch with scale factor 1/a) Look at the example below – graphs of y = sinxand y = sin2x

  6. Translation Assuming we know the shape and form of the graph of y = f(x) …. … The graph of y = f(x) + a is a vertical shiftof this graph by +a Look at the example below – graphs of y = sinxand y = sinx + 3 and y = sinx – 2

  7. Translation (continued) Assuming we know the shape and form of the graph of y = f(x) …. … The graph of y = f(x + a) is a horizontal shiftof this graph by ∓a Look at the example below – graphs of y = x2and y = (x – 3)2 and y = (x + 2)2

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