Linear, Exponential vs. Quadratic Functions: What’s the difference?

Mr. Bayes doing a first order Taylor approximation of Linear, Exponential and Quadratic functions.

A guide on 3 common algebra functions used in data science and data analysis, with worked examples using cats 😺

1. Linear Functions

Linear functions are those whose graph is a straight line in the coordinate plane. It has the following form where x is the independent variable (also called the input) and y is the dependent variable (i.e. the output) :

Linear function formula, x = independent variable (i.e. input), y = dependent variable (i.e. output)

• a is the slope (also known as gradient, coefficient) of the independent variable x. It decides how quickly a change in x impacts a change in y
• b is the intercept (also known as the constant). It is the value of y when x = 0 and can be visualised as the y-axis intercept

A simple example of linear functions

You adopted a kitten, 3-month-old Mr. Whiskers from the local animal shelter and he weighed 500g when you picked him up. During the following period, you notice that he gains ~ 200g per month. How much can you expect Mr. Whiskers to weigh when he turns 12 months old?