Using translations, it is found that the equation the represents the graphed function is:
[tex]y = -f(x) - 3[/tex], given by option C.
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- The parent function is [tex]f(x) = \sqrt{x}[/tex].
- As x increases, it's value increases. In the graph, as x increases, it decreases, thus it was multiplied by -1, that is, [tex]-f(x)[/tex].
- The parent function is defined for [tex]x \geq 0[/tex], and the same is valid for the function in the graph, thus we have [tex]f(x)[/tex] and not [tex]f(-x)[/tex].
- The initial value of the parent function is [tex]y = 0[/tex], here it is [tex]y = -3[/tex], thus it was shifted down 3 units, that is, [tex]y = -f(x) - 3[/tex], and the correct option is C.
A similar problem is given at https://brainly.com/question/17072859
