The function graphed is option D. [tex]f(x) = \sqrt{(x+4)}[/tex], the function is translated 4 times horizontally to the left.
How to find the function which was used to make graph?
There are many tools we can use to find the information of the relation which was used to form the graph.
A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.
The function is translated horizontally to the left. the base function is [tex]y = \sqrt{x}[/tex].
A. f(x) [tex]\sqrt{(x-5)} + 1[/tex], the graph should be translated horizontally 5 units to the right.
It's not the case and the translated 1 unit vertically.
B. [tex]f(x) = \sqrt{(x-2)}[/tex] the graph should be translated horizontally 2 units to the right. It's not the case.
C. [tex]y = \sqrt{x}[/tex], the graph should start at x=0. It's not the case.
D. [tex]f(x) = \sqrt{(x+4)}[/tex], the function is translated 4 times horizontally to the left. So this is the case.
Therefore, the function graphed is option D. [tex]f(x) = \sqrt{(x+4)}[/tex], the function is translated 4 times horizontally to the left.
Learn more about finding the graphed function here:
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