In Exercises 107-118, begin by graphing the cube root function, f(x) = ∛x. Then use transformations of this graph to graph the given function. -∛(x+2)

The cube root function, denoted as f(x) = ∛x, is a type of radical function that returns the number which, when cubed, gives the input x. This function is defined for all real numbers and has a characteristic S-shaped curve that passes through the origin (0,0). Understanding its basic shape and properties is essential for applying transformations.

Graph transformations involve shifting, reflecting, stretching, or compressing the graph of a function. In this case, the transformation involves a vertical reflection and a horizontal shift. Specifically, the function -∛(x+2) reflects the cube root function across the x-axis and shifts it left by 2 units, altering its position and orientation.

Function notation, such as f(x), represents a relationship between input values (x) and output values (f(x)). Evaluating a function involves substituting specific x-values into the function to find corresponding outputs. Understanding how to manipulate and evaluate functions is crucial for accurately graphing transformed functions and interpreting their behavior.