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)

Key Concepts

Cube Root Function

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

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 and Evaluation

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.