Basic Algebra Part 3— Functions
Welcome to the third and a very brief post on functions. In the first part of Basic Algebra we learnt about the basic equations and then went on to learn about Exponents, Logarithm and Polynomial Equations in the second part.
In this blog, let’s see what is a function? Simply put, function is something that processes an input and produces an output.
It can be any sort of relationship between the input and the corresponding output. For example, we can have “square” as a function. If X is an input, the output of the function “square”, will always be “X-Squared.
So we can say that,
This is how the function is represented as. Function can take any form and shape as long as it processes the input.
If you remember we talked about the age of the student based on the grade she is studying in. So can we say that age is a function of grade, where
Age = Grade + 5
However, as you would have noticed, we restricted the values of grade between 1 and 10, because if we extend this line, it does not make sense for the grades such as pre-primary and definitely not the negative age.
So every function also has got some limits and allowed values.
Let’s see another function which is
Now if the value of X here is 1, the denominator will become zero and the output of the function becomes undefined or infinity, as we can not divide any number by zero. So irrespective of whether the X is positive or negative, it can never take a value of 1.
We can find all possible combinations for other values of X and as the value of X increases, the function approaches almost zero.
However, such a function is not a continuous function. For a continuous function, we should be able to draw it without lifting the pen. This is good enough to know about the functions.
Summary
so in this short blog, we saw what is a function, how the relationship can be defined as a function, what are the allowed values and what is a continuous function. Typically, every machine learning problem tries to predict something, it could be revenue or demand of a product in case of regression problem or whether a customer will buy my product or not type of classification problems. In all such cases, the prediction becomes a function of input variables or as they may say features. Hence, it is important to know what is a function.
Enjoy your time…
