The transformation of a function may involve any change in the function. The value of the function g(x) will be 6|x|+10.
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:
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(\dfrac{x}{k})
Given the function f(x)=3|x|+5, therefore, if the function is vertically stretched by a factor of 2, then the function g(x) can be written as,
g(x) = 2[f(x)]
g(x) = 2(3|x|+5)
g(x) = 6|x| + 10
Hence, the value of the function g(x) will be 6|x|+10.
Learn more about Transforming functions:
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