the graph shows the function f(x). which equation represents f(x)? o f(x)=-\\sqrt3{x} o f(x)=-\\sqrt3{x - 1}…

the graph shows the function f(x). which equation represents f(x)? o f(x)=-\\sqrt3{x} o f(x)=-\\sqrt3{x - 1} o f(x)=\\sqrt3{-x}-1 o f(x)=\\sqrt3{-x}

the graph shows the function f(x). which equation represents f(x)? o f(x)=-\\sqrt3{x} o f(x)=-\\sqrt3{x - 1} o f(x)=\\sqrt3{-x}-1 o f(x)=\\sqrt3{-x}

Answer

Explanation:

Step1: Analyze the key - point of the graph

The graph passes through the origin ((0,0)). We can test each option by substituting (x = 0) into the functions.

Step2: Test option 1

For (f(x)=-\sqrt[3]{x}), when (x = 0), (f(0)=-\sqrt[3]{0}=0).

Step3: Test option 2

For (f(x)=-\sqrt[3]{x - 1}), when (x = 0), (f(0)=-\sqrt[3]{0 - 1}=-\sqrt[3]{-1}=1\neq0).

Step4: Test option 3

For (f(x)=\sqrt[3]{-x}-1), when (x = 0), (f(0)=\sqrt[3]{0}-1=-1\neq0).

Step5: Test option 4

For (f(x)=\sqrt[3]{-x}), when (x = 0), (f(0)=\sqrt[3]{0}=0). Also, note the shape of the cube - root function (y = \sqrt[3]{x}) is symmetric about the origin. The function (y=\sqrt[3]{-x}=-\sqrt[3]{x}) is a reflection of (y = \sqrt[3]{x}) across the (y) - axis, which matches the given graph.

Answer:

(f(x)=\sqrt[3]{-x})