# Functions

What is a function? How can you describe a function? What are the most important standard functions?

### Mathematical modeling

The Nuna solar car is used as an example to show the cycle of mathematical modeling: A real-world problem is described mathematically using functions. Equations help to solve these problems in order to make predictions in the real-world.

### What is a function?

What is a function? A function is a rule that relates two given sets: to each object of one set, it associates precisely one object from the other set.You will learn to see a mathematical function as a machine performing an operation on an input and learn about domain and codomain.

### How to describe a function?

You can describe a function in words, as a graph, a table and a formula. You will learn the advantages and disadvantages of each method.

### Polynomial functions

A polynomial function is a function that can be constructed from a variable and a set of numbers, using only addition and multiplication. You will learn how to determine the degree of a polynomial.

### Rational functions

A rational function is a function that can be constructed from a variable and a set of numbers, using addition, multiplication and division. A rational function can be written as the ratio of two polynomial functions.

### Graphs of polynomial functions

The graphs of polynomial functions have certain characteristics depending on the degree of the polynomial. This video tells you what the graph of a polynomial looks like.

### Power functions

What is a power function? A power function is a function of the form x to the power a with ‘a’ a constant, called the exponent. In this video we will look at power functions with integer exponents.

### Power functions with non-integer exponents

What is a power function? A power function is a function of the form x to the power a with ‘a’ a constant, called the exponent. In this video we will look at power functions with non-integer exponents.

### Continuous functions

What is continuity? A function is called continuous when a small change on the horizontal axis will give only a small change on the vertical axis.

### Domain and range

What is the domain, codomain and range of a function? What number can you put in a function and what is the influence of the context?

### Summary about functions - part 1

What is a function? What are polynomial, rational and power functions? This video gives the summary of week 1 of the edX course: pre-university Calculus (Calc001x)

### Definition of trigonometric functions

The trigonometric functions are usually defined as the ratio of two sides in a rectangular triangle. The sine, cosine and tangent are explained using a geometric representation and the unit circle.

### Trigonometric functions - rules of calculation

Using the Pythagorean Theorem, the unit circle and a geometric representation, the rules of calculation for the sine, cosine and tangent are explained.

### Composing functions

Functions can be composed by applying a function to another function. This concept is very important to understanding the chain rule in differentiation.

### Scaling and Translation

Functions can be composed by applying a function to another function. In this video we look at the graphs of composed functions and the effects of scaling and translation.

### Exponential functions

An exponential function has the form f(x) = A b^x. Here A is some nonzero constant, and b is a positive number called the base of the exponential function.The number x is called the exponent. You will learn about the characteristics and graphs of exponential functions.

### Inverse functions

What is an inverse function? How can you use the horizontal line test to determine whether a function has an inverse function? How to determine the domain and range of an inverse function?

### Logarithms

A logarithm is the inverse function of an exponential function. You will learn the common bases for logarithms.

### Logarithms - rules of calculation

In this video the rules of calculation for exponential functions are used to find the rules of calculation for logarithms.

### Inverse trigonometric functions

Remember inverse functions? In this video you will learn about the inverse functions of the trigonometric functions: sine, cosine and tangent.

### Summary about functions - part 2

What are the properties of trigonometric functions: the sine, cosine and tangent? What is an exponential function and what is the inverse of the exponential function: the logarithm? This video gives the summary of week 2 of the edX course: pre-university Calculus (Calc001x)