Write a function g whose graph represents a vertical shrink by a factor of 1/2 of the graph of f(x)=2x+6.

Question

Write a function g whose graph represents a vertical shrink by a factor of 1/2 of the graph of f(x)=2x+6.

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Thiên Thanh 3 weeks 2023-01-14T17:32:28+00:00 1 Answer 0 views 0

Answer ( 1 )

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    2023-01-14T17:33:38+00:00
    The function g(x) which is a vertical shrink by a factor of 1/2 of the graph of f(x) is equal to g(x)=x+4.5.

    How does the transformation of a function happen?

    The transformation of a function may involve any change.
    Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
    If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
    Horizontal shift (also called phase shift):
    • Left shift by c units, y=f(x+c) (same output, but c units earlier)
    • Right shift by c units, y=f(x-c)(same output, but c units late)
    Vertical shift
    • Up by d units: y = f(x) + d
    • Down by d units: y = f(x) – d
    Stretching:
    • Vertical stretch by a factor k: y = k × f(x)
    • Horizontal stretch by a factor k: y = f(x/k)
    Given that the graph of f(x)=2x+6 needed to be vertical shrink by a factor of 1/2 is,
    g(x) = (1/2)  × f(x)
    g(x) = (1/2) × (2x + 6)
          = [(1/2) ×2x] + [(1/2) ×9]
          = x + 4.5
    Hence, the function g(x) which is a vertical shrink by a factor of 1/2 of the graph of f(x) is equal to g(x)=x+4.5.
    Learn more about Transforming functions here:
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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )