Exploring Functions: From Algebra to Real Life

Exploring Functions: From Algebra to Real Life

Learning Objective

Understand functions, continuity, one-to-one, and onto mappings.

What do you already know about functions and their real-life applications?

What is a Function?

A function is a relation that assigns each input exactly one output.

Function Notation

Functions can be represented using f(x) = 2x + 3, where x is the input and 2x + 3 is the output.

Continuity of Functions

A function is continuous if it can be drawn without lifting the pen from the paper.

One-to-One Functions

A function is one-to-one if each output value is paired with exactly one input value.

Onto Functions

A function is onto if every element in the codomain is the image of at least one element in the domain.

Real-life Examples

Functions are prevalent in everyday life, such as in finance, engineering, and biology.

Differentiated Activities

Low level: Guided practice with step-by-step instructions. On level: Application of functions to real-life scenarios. Advanced: Advanced problem-solving and proof of one-to-one and onto functions.

Write down 3 things you learned in this lesson.

Have students enter three things they learned in this lesson. With this they can indicate their own learning efficiency of this lesson.

Write down 2 things you want to know more about.

Here, students enter two things they would like to know more about. This not only increases involvement, but also gives them more ownership.

Ask 1 question about something you haven't quite understood yet.

The students indicate here (in question form) with which part of the material they still have difficulty. For the teacher, this not only provides insight into the extent to which the students understand/master the material, but also a good starting point for the next lesson.