Answer:
The correct option is 3.
Step-by-step explanation:
The parent cube root function is
[tex]g(x)=\sqrt[3]{x}[/tex]
From the given graph it is clear that the graph of f(x) is transformed by reflecting the graph of g(x) across y-axis and shifting two units down.
If the parent cube root function is reflected across the y-axis, then x is replaced by -x.
[tex]g(-x)=\sqrt[3]{-x}[/tex]
Now, the graph of new function sifts 1 unit down. So, the required function is
[tex]f(x)=\sqrt[3]{-x}-1[/tex]
The graph shows the function [tex]f(x)=\sqrt[3]{-x}-1[/tex].
From the given graph it is clear that the graph passes through the points (-8,1), (0,-1) and (8,-3).
Check the above function by these points.
At x=-8,
[tex]f(-8)=\sqrt[3]{-(-8)}-1=2-1=1[/tex]
At x=0,
[tex]f(0)=\sqrt[3]{-(0)}-1=0-1=-1[/tex]
At x=8,
[tex]f(8)=\sqrt[3]{-(8)}-1=-2-1=-3[/tex]
All these points satisfy by the abobe function. It means the above function is correct.
Therefore the correct option is 3.
