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 = \sqrt[3]{x+8}) is a transformation of the parent cube - root function (y=\sqrt[3]{x}). The domain of (y = \sqrt[3]{x+8}) is all real numbers since we can take the cube - root of any real number. The general form of a cube - root function (y = a\sqrt[3]{x - h}+k) (in our case (a = 1), (h=-8), (k = 0)).

Step2: Determine the behavior of the function

The cube - root function (y=\sqrt[3]{x}) has a positive slope for all real (x) values. For the function (y=\sqrt[3]{x + 8}), as (x) increases, (y) also increases. There are no intervals where the function is decreasing.

Answer:

The function is always increasing.