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. g(x) = ∛x+2

Key Concepts

Cube Root Function

The cube root function, f(x) = ∛x, is a fundamental mathematical function that returns the number whose cube is x. It 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 graphing transformations.

Graph Transformations

Graph transformations involve shifting, stretching, compressing, or reflecting the graph of a function. In this case, the transformation applied to the cube root function to obtain g(x) = ∛(x + 2) is a horizontal shift to the left by 2 units. Recognizing how these transformations affect the graph is crucial for accurately sketching the new function.

Function Notation

Function notation, such as f(x) and g(x), is a way to represent functions and their outputs. It allows for clear communication of the relationship between input values (x) and their corresponding outputs (f(x) or g(x)). Understanding function notation is vital for interpreting and manipulating functions correctly in algebra.