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1.4 Transformations

1.4 Transformations. Vertical Shifts : y = f (x) + c UP c units y = f (x) – c DOWN c units. 1.4 Transformations. Horizontal Shifts : y = f (x – b) RIGHT b units y = f (x + b) LEFT b units. 1.4 Transformations. Reflections : y = – f (x)

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1.4 Transformations

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  1. 1.4 Transformations • Vertical Shifts: • y = f(x) + c • UP c units • y = f(x) – c • DOWN c units

  2. 1.4 Transformations • Horizontal Shifts: • y = f(x – b) • RIGHT b units • y = f(x + b) • LEFT b units

  3. 1.4 Transformations • Reflections: • y = – f(x) • f(x) reflects in x-axis • y = f(– x) • f(x) reflects in y-axis

  4. Vertical Stretch & Shrink: • y = af(x) a > 1 • Stretches vertically by a factor of a • y = af(x) 0 < a < 1 • Shrinks vertically by a factor of a

  5. Horizontal Stretch & Shrink: • y = f(mx) m > 1 • Shrinks horizontally by a factor of m • y = f(mx) 0 < m < 1 • Stretches horizontally by a factor of m

  6. f(x) • Ex 1: Given y = f(x)

  7. Ex 1: Sketch • y = −f(x+2) • y = 2f(x)−1

  8. Ex 2: Sketch f(x) and use it to sketch g(x). • f(x) = x2 • g(x) = (x+1) 2 + 2

  9. Ex 3: Write g(x) given the following transformations of f(x). • f(x) = |x| • Left 1 • Up 6 • Reflect in x-axis • Horizontal Stretch by a factor of ½

  10. HW – 1.4 pg. 48 # 1 – 13 EOO, #15 – 19 odds # 21 – 37 EOO, # 43 – 55 EOO, # 61, & 63

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