Intuiting Functions
A function is a scribble that crosses each vertical line only once.
This post is part of the series An Intuitive Primer on Calculus.
A function is a scribble that crosses each vertical line only once.
![image](https://justinmath.com/files/blog/function-vs-not-function.png)
The instructions for drawing a function are given by the function’s equation. Each vertical line is labeled with a number, and when you plug that number into the $x$ variable in a function, the result tells you how high the function should be when it crosses that line.
For example, to draw the function whose equation is $y=3x+1$, we can start by plugging in the numbers $-1,$ $0,$ and $1.$
Our results mean:
- On the line $x=-1,$ the scribble needs to cross at height $y=-2.$
- On the line $x=0$, the scribble needs to cross at height $y=1.$
- On the line $x=1,$ the scribble needs to cross at height $y=4.$
In other words, we need to plot the points $(-1,-2),$ $(0,1),$ and $(1,4)$ on the grid. Since this is a linear function, we can draw the rest of the function just by connecting the dots.
![image](https://justinmath.com/files/blog/connect-dots-linear-function.png)
Linear functions are straight lines, but in general, functions tend to be curvy. There are many different types of functions, each of whose scribble curves in a different way.
This post is part of the series An Intuitive Primer on Calculus.