Determine whether each function graphed or defined is one-to-one. y = ∛x+1 - 3

Key Concepts

One-to-One Functions

A function is considered one-to-one if it assigns a unique output for every unique input, meaning no two different inputs produce the same output. This can be tested using the horizontal line test: if any horizontal line intersects the graph of the function more than once, the function is not one-to-one.

Cubic Root Function

The cubic root function, represented as y = ∛x, is a type of radical function that returns the number which, when cubed, gives the input value x. This function is defined for all real numbers and is continuous and increasing, which contributes to its one-to-one nature.

Transformations of Functions

Transformations involve shifting, reflecting, stretching, or compressing the graph of a function. In the given function y = ∛x + 1 - 3, the transformations include a vertical shift of +1 and a downward shift of -3, which do not affect the one-to-one property of the original cubic root function.