the graph of f(x) = ∛(x + 8) is shown. which statement is true? the function is only increasing when x ≥ -8…

the graph of f(x) = ∛(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) = ∛(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: Analyze the domain

The cube - root function $y = \sqrt[3]{x + 8}$ has a domain of all real numbers since we can take the cube - root of any real number. The expression inside the cube - root, $x+8$, can be any real number.

Step2: Examine the slope of the graph

The general form of a cube - root function $y=\sqrt[3]{x}$ has a positive slope for all real $x$ values. For the function $y = \sqrt[3]{x + 8}$, it is a horizontal shift of $y=\sqrt[3]{x}$ by 8 units to the left. Looking at the graph, as $x$ increases, the value of $y=\sqrt[3]{x + 8}$ also increases for all real $x$ values.

Answer:

The function is always increasing.