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

the graph of f(x) = \\sqrt3{x + 8} is shown. which statement is true? the function is only increasing when x ≥ -8. the function is only increasing when x ≥ 0. 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 x ≥ -8. the function is only increasing when x ≥ 0. the function is always decreasing. the function is always increasing.

Answer

Explanation:

Step1: Recall the property of cube - root function

The function (y = \sqrt[3]{u}) is an increasing function for all real - valued (u). For the function (f(x)=\sqrt[3]{x + 8}), let (u=x + 8).

Step2: Analyze the domain and monotonicity

The domain of (f(x)=\sqrt[3]{x + 8}) is all real numbers since we can take the cube - root of any real number. As (x) increases, (u=x + 8) increases, and since (y=\sqrt[3]{u}) is an increasing function, (y = f(x)) increases for all real (x).

Answer:

The function is always increasing.