the graph of (f(x)=sqrt3{x + 8}) is shown. which statement is true? the function is only increasing when…

the graph of (f(x)=sqrt3{x + 8}) is shown. which statement is true? the function is only increasing when (xgeq - 8). the function is only increasing when (xgeq0). the function is always decreasing. the function is always increasing.

the graph of (f(x)=sqrt3{x + 8}) is shown. which statement is true? the function is only increasing when (xgeq - 8). the function is only increasing when (xgeq0). the function is always decreasing. the function is always increasing.

Answer

Explanation:

Step1: Analyze the cube - root function

The function (y = f(x)=\sqrt[3]{x + 8}) is a transformation of the basic cube - root function (y=\sqrt[3]{x}). The domain of the cube - root function is all real numbers, and its derivative (y^\prime=\frac{1}{3(x + 8)^{\frac{2}{3}}}>0) for all (x\neq - 8).

Step2: Check the behavior of the function

Since the derivative of (y = \sqrt[3]{x+8}) is positive for all real - valued (x) (the cube - root function is continuous everywhere), the function is always increasing.

Answer:

The function is always increasing.