Answer:
[tex]\textsf{A)}\quad y=\sqrt[3]{x+2}-1[/tex]
Step-by-step explanation:
The graph of the function resembles that of a cube root function as it is an S-shaped function that approaches negative infinity as x approaches negative infinity, and approaches positive infinity as x approaches positive infinity.
The parent cube root function y = ∛x is symmetric about the origin (0, 0) and has a point of inflection at the origin (0, 0).
The point of inflection of the graphed function is at (-2, -1). This means that the parent cube root graph has been translated 2 units left and 1 unit down.
When we translate a function n units left, we add n to the x-variable, and when we translate a function n units down, we subtract n from the function.
Therefore, the equation of the graphed function is answer option A:
[tex]\Large\boxed{\boxed{y=\sqrt[3]{x+2}-1}}[/tex]
