Q:

PLEASE SOMEONE HELP ME PLATO:If the parent function f(x) = [3]\sqrt[n]{x} is transformed to g(x) =[3]\sqrt[n]{x+2-4] , which is the graph of g(x)?

Accepted Solution

A:
Answer:(A)Step-by-step explanation:The graph of any function (of [tex]x[/tex]) can be shifted horizontally by a number [tex]h[/tex] by replacing every [tex]x[/tex] in the function with [tex]x - h[/tex]. And, if we want to shift the graph vertically, we simply add the number we want to shift by (which I'll call [tex]k[/tex]) to every output of the function.Functionally, if we have any function [tex]f(x)[/tex]We can shift it horizontally by [tex]h[/tex] units and vertically by [tex]k[/tex] units by creating a function [tex]g(x) = f(x - h) + k[/tex].Notice that in this case, [tex]g(x) = f(x - (-2)) - 4[/tex]. So the graph of [tex]f(x)[/tex] is shifted 2 units to the left, and 4 units down.Or if this is too abstract of an explanation, then notice[tex]\sqrt[3]{x + 2} Β - 4[/tex] looks similar to [tex]\sqrt[3]{x - h} Β - k[/tex]. Specifically, if h = -2 and k = -4 (the graph is shifted two units left and 4 units down), then the function becomes equivalent to [tex]g(x)[/tex]