What is a function? What is a one-to-one function? Using examples of domain and range and looking at different mappings, this video looks at the definition of a function and more specifically, the definition of a one-to-one function.

Video first reviews what the null space is and how to solve for it using reduced row echelon form. Shows that any solution to the inhomogeneous system Ax = b will be the sum of a particular solution and a homogeneous solution. Extends...

Video first reviews that a function is invertible if and only if there is a unique solution to f(x) = y for any y. Extends this to show that a function is invertible if and only if it is surjective (onto) and injective (one-to-one). [6:31]

Video explains what a surjective or onto function is and also what an injective or one-to-one function is. Gives examples and non-examples of surjective and injective functions. [9:31]

Relating invertibility to being onto (surjective) and one-to-one (injective)

The video resource shows worked examples of algebra concepts. Students watch a detailed problem on how to determine if the points on a graph represent a function. [2:23]

Introduction to surjective and injective functions with examples.