The base graph has been shifted down 2 units.
g(x) = f(x) -2 and that -2 is outside the f(x) notation, so it's an up/down transformation. -2 says "move it down 2 units."
A transformation of the function f(x) = |x| by observing the equation of the function g(x) = |x|- 2 is option B; The base graph has been shifted down 2 units.
The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming horizontal axis is input axis and 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:
[tex]y = k \times f(x)[/tex]
Horizontal stretch by a factor k:
[tex]y = f\left(\dfrac{x}{k}\right)[/tex]
We have g(x) = f(x) -2 and that -2 is outside the f(x) notation,
Thus, it's an up/down transformation -2 says "move it down 2 units."
Therefore, The base graph has been shifted down 2 units.
Hence, A transformation of the function f(x) = |x| by observing the equation of the function g(x) = |x|- 2 is option B.
Learn more about transforming functions here:
https://brainly.com/question/17006186
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