Graph each function. See Examples 6–8 and the Summary of Graphing Techniques box following Example 9. ƒ(x)=3√x-2

Key Concepts

Graphing Functions

Graphing functions involves plotting points on a coordinate plane to visually represent the relationship between the input (x) and output (f(x)). Understanding how to identify key features such as intercepts, asymptotes, and behavior at infinity is essential for accurately depicting the function's shape.

Cube Root Function

The cube root function, represented as f(x) = 3√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 shape that increases gradually, crossing the origin and having a domain and range of all real numbers.

Transformations of Functions

Transformations of functions involve shifting, stretching, or reflecting the graph of a function. In the given function f(x) = 3√x - 2, the '-2' indicates a vertical shift downward by 2 units, which alters the graph's position without changing its shape. Understanding these transformations is crucial for accurately graphing modified functions.