Respuesta :

The graph of the parent cube root function which is [tex]y= \sqrt[3]{x} [/tex]  passes from the origin. We have to find the graph of [tex]y=\sqrt[3]{x-5} [/tex]

Addition or subtraction of a number from the function argument i.e. x, shifts the graph horizontally. Addition of a number to the arguments moves it to left, while subtraction of a number moves it to right. 5 is being subtracted from the function argument x. This means the graph of parent cube root function will be shifted 5 units to the left without any change in the vertical direction.

The final picture shows such a graph. So the correct answer is option D 
JeanaShupp

Answer: Fourth graph

Step-by-step explanation:

The given function is [tex]y=\sqrt[3]{x-5}[/tex]

To find the x intercept of the graph, put y=0, we get

[tex]0=\sqrt[3]{x-5}\\\\\Rightarrow x-5=0\\\\\Rightarrow\ x=5[/tex]

We we look in the given graphs only in the fourth graph the curve is passing through x intercept (5,0) .

Therefore, the fourth graph  represents  [tex]y=\sqrt[3]{x-5}[/tex].

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