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)

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