The equation for the function graphed above is [tex]g(x) = |x-2| + 1[/tex].
The expression of [tex]g(x)[/tex] is the consequence of translating both horizontally and vertically regarding [tex]f(x)[/tex], which it can be defined by following expression:
[tex]g(x) = f(x - h) + k[/tex] (1)
- [tex]f(x)[/tex] - Original function.
- [tex]g(x)[/tex] - Resulting function.
- [tex](h,k)[/tex] - Coordinates of the "center" of the resulting function.
If we know that [tex](h,k) = (2, 1)[/tex] and [tex]f(x) = |x|[/tex], then the resulting function is:
[tex]g(x) = |x-2| + 1[/tex]
The equation for the function graphed above is [tex]g(x) = |x-2| + 1[/tex].
