The transformation of a function may involve any change. The correct option is 2. The value will be g(x) = log₂(x+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 \times f(x)
Horizontal stretch by a factor k: y = f\left(\dfrac{x}{k}\right)
As we know to shift a function towards the left horizontally, we need to add the number of units to the value of x. Therefore, the function of g(x) will be written as,
g(x) = log₂(x+5)
Hence, the correct option is 2. The value will be g(x) = log₂(x+5).
Learn more about Transforming functions:
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